<PAGE>   1
                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

                          ----------------------------

                                    FORM 10-Q

(MARK ONE)

[x]      QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES
         EXCHANGE ACT OF 1934

For the quarterly period ended     March 31, 1997
                               -----------------------------

                                       OR

[ ]      TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES
         EXCHANGE ACT OF 1934

For the transition period from                         to
                                  ------------------       -----------------

                       Commission File Number     0-18495
                                                ------------

Enstar Income/Growth Program Six-B, L.P.
-------------------------------------------------------------------------------
             (Exact name of Registrant as specified in its charter)

                          Georgia                              58-1754588
---------------------------------------------------   -------------------------
      (State or other jurisdiction of incorporation        (I.R.S. Employer 
                     or organization)                  Identification Number)

           10900 Wilshire Boulevard - 15th Floor
                  Los Angeles, California                      90024
--------------------------------------------------       ----------------------
          (Address of principal executive offices)           (Zip Code)

Registrant's telephone number, including                  (310) 824-9990
area code:                                           --------------------------


-------------------------------------------------------------------------------
Former name, former address and former fiscal year, if changed since last
report.



         Indicate by check mark whether the registrant (1) has filed all reports
required to be filed by Section 13 or 15(d) of the Securities Exchange Act of
1934 during the preceding 12 months (or for such shorter period that the
registrant was required to file such reports), and (2) has been subject to such
filing requirements for the past 90 days. Yes  X  No
                                             -----  -----


<PAGE>   2
                         PART I - FINANCIAL INFORMATION

                    ENSTAR INCOME/GROWTH PROGRAM SIX-B, L.P.

                            CONDENSED BALANCE SHEETS

                    ========================================

<TABLE>
<CAPTION>
                                                                     December 31,        March 31,
                                                                        1996*              1997
                                                                     ------------     ------------
                                                                                       (Unaudited)
<S>                                                                  <C>              <C>        
ASSETS:
   Cash and cash equivalents                                         $   353,500      $   205,200
   Accounts receivable, less allowance of $1,900 and
      $3,500 for possible losses                                          67,200           81,300
   Insurance claim receivable                                            250,500             --
   Prepaid expenses and other assets                                      61,600           57,900
   Property, plant and equipment, less accumulated
      depreciation and amortization of $2,621,500 and $2,778,300       3,593,400        3,574,400
   Franchise cost, net of accumulated
      amortization of $2,256,400 and $2,346,100                        2,053,300        1,961,700
   Intangible costs, net of accumulated amortization
      of $322,300 and $337,900                                           277,000          263,500
                                                                     -----------      -----------
                                                                     $ 6,656,500      $ 6,144,000
                                                                     ===========      ===========

                                    LIABILITIES AND PARTNERSHIP CAPITAL
                                    -----------------------------------
LIABILITIES:
   Accounts payable                                                  $   145,700      $   181,600
   Due to affiliates                                                   1,679,000        1,108,500
   Note payable                                                        1,288,400        1,288,400
                                                                     -----------      -----------
          TOTAL LIABILITIES                                            3,113,100        2,578,500
                                                                     -----------      -----------

COMMITMENTS AND CONTINGENCIES

PARTNERSHIP CAPITAL (DEFICIT):
   General partners                                                      (37,200)         (37,000)
   Limited partners                                                    3,580,600        3,602,500
                                                                     -----------      -----------
          TOTAL PARTNERSHIP CAPITAL                                    3,543,400        3,565,500
                                                                     -----------      -----------
                                                                     $ 6,656,500      $ 6,144,000
                                                                     ===========      ===========
</TABLE>


               *As presented in the audited financial statements.

            See accompanying notes to condensed financial statements.

                                      -2-

<PAGE>   3
                    ENSTAR INCOME/GROWTH PROGRAM SIX-B, L.P.

                       CONDENSED STATEMENTS OF OPERATIONS

                    ========================================


<TABLE>
<CAPTION>
                                                   Unaudited
                                           ------------------------
                                             Three months ended
                                                  March 31,
                                           ------------------------
                                              1996           1997
                                           ---------      ---------
<S>                                        <C>            <C>      
REVENUES                                   $ 575,200      $ 730,800
                                           ---------      ---------
OPERATING EXPENSES:
   Service costs                             189,100        240,100
   General and administrative expenses        97,900        100,100
   General Partner management fees
      and reimbursed expenses                 54,200         66,300
   Depreciation and amortization             211,600        271,200
                                           ---------      ---------
                                             552,800        677,700
                                           ---------      ---------
OPERATING INCOME                              22,400         53,100
                                           ---------      ---------

OTHER INCOME (EXPENSE):
   Interest income                             1,300          2,100
   Interest expense                          (39,200)       (33,100)
                                           ---------      ---------
                                             (37,900)       (31,000)
                                           ---------      ---------
NET INCOME (LOSS)                          $ (15,500)     $  22,100
                                           =========      =========

NET INCOME (LOSS) PER UNIT OF LIMITED
   PARTNERSHIP INTEREST                    $    (.42)     $     .60
                                           =========      =========

AVERAGE LIMITED PARTNERSHIP
   UNITS OUTSTANDING DURING PERIOD            36,626         36,626
                                           =========      =========
</TABLE>




            See accompanying notes to condensed financial statements.

                                      -3-
<PAGE>   4
                    ENSTAR INCOME/GROWTH PROGRAM SIX-B, L.P.

                            STATEMENTS OF CASH FLOWS

                    ========================================


<TABLE>
<CAPTION>
                                                                      Unaudited
                                                              ------------------------
                                                                 Three months ended
                                                                      March 31,
                                                              ------------------------
                                                                 1996           1997
                                                              ---------      ---------
<S>                                                           <C>            <C>      
CASH FLOWS FROM OPERATING ACTIVITIES:
   Net income (loss)                                          $ (15,500)     $  22,100
   Adjustments to reconcile net income (loss) to net cash
      provided by operating activities:
       Depreciation and amortization                            211,600        271,200
       Amortization of deferred loan costs                         --              500
       Increase from changes in:
         Receivables                                              1,800        236,400
         Prepaid expenses and other assets                        8,500          3,700
         Accounts payable                                        17,400         35,900
                                                              ---------      ---------
             Net cash provided by operating activities          223,800        569,800
                                                              ---------      ---------
CASH FLOWS FROM INVESTING ACTIVITIES:
   Capital expenditures                                         (49,800)      (147,200)
   Increase in intangible assets                                 (4,100)          (400)
                                                              ---------      ---------
             Net cash used in investing activities              (53,900)      (147,600)
                                                              ---------      ---------
CASH FLOWS FROM FINANCING ACTIVITIES:
   Due to affiliates                                            131,700       (570,500)
                                                              ---------      ---------
INCREASE (DECREASE) IN CASH AND CASH
   EQUIVALENTS                                                  301,600       (148,300)

CASH AND CASH EQUIVALENTS
   AT BEGINNING OF PERIOD                                        39,800        353,500
                                                              ---------      ---------
CASH AND CASH EQUIVALENTS
   AT END OF PERIOD                                           $ 341,400      $ 205,200
                                                              =========      =========
</TABLE>




            See accompanying notes to condensed financial statements.

                                      -4-
<PAGE>   5
                    ENSTAR INCOME/GROWTH PROGRAM SIX-B, L.P.

                     NOTES TO CONDENSED FINANCIAL STATEMENTS

                    ========================================


1.       INTERIM FINANCIAL STATEMENTS

         The accompanying condensed interim financial statements for the three
months ended March 31, 1997 and 1996 are unaudited. These condensed interim
financial statements should be read in conjunction with the audited financial
statements and notes thereto included in the Partnership's latest Annual Report
on Form 10-K. In the opinion of management, such statements reflect all
adjustments (consisting only of normal recurring adjustments) necessary for a
fair presentation of the results of such periods. The results of operations for
the three months ended March 31, 1997 are not necessarily indicative of results
for the entire year.

2.       TRANSACTIONS WITH THE GENERAL PARTNER AND AFFILIATES

         The Partnership has a management and service agreement with a wholly
owned subsidiary of the Corporate General Partner (the "Manager") for a monthly
management fee of 5% of revenues, excluding revenues from the sale of cable
television systems or franchises. Management fee expense approximated $36,600
for the three months ended March 31, 1997.

         In addition to the monthly management fee described above, the
Partnership reimburses the Manager for direct expenses incurred on behalf of the
Partnership and for the Partnership's allocable share of operational costs
associated with services provided by the Manager. All cable television
properties managed by the Corporate General Partner and its subsidiary are
charged a proportionate share of these expenses. Corporate office allocations
and district office expenses are charged to the properties served based
primarily on the respective percentage of basic subscribers or homes passed
(dwelling units within a system) within the designated service areas. The total
amount charged to the Partnership for these services approximated $29,700 for
the three months ended March 31, 1997. Management fees and reimbursed expenses
due the Corporate General Partner are non-interest bearing.

         The Partnership also receives certain system operating management
services from affiliates of the Corporate General Partner in addition to the
Manager due to the fact that there are no such employees directly employed by
the Partnership. The Partnership reimburses the affiliates for its allocable
share of the affiliates' operational costs. The total amount charged to the
Partnership for these costs approximated $61,200 for the three months ended
March 31, 1997. No management fee is payable to the affiliates by the
Partnership and there is no duplication of reimbursed expenses and costs paid to
the Manager.

         Certain programming services have been purchased through an affiliate
of the Partnership. In turn, the affiliate charges the Partnership for these
costs based on an estimate of what the Corporate General Partner could negotiate
for such programming services for the 15 partnerships managed by the Corporate
General Partner as a group. The Partnership recorded programming fee expense of
$131,200 for the three months ended March 31, 1997. Programming fees are
included in service costs in the statements of operations.


                                      -5-
<PAGE>   6
                    ENSTAR INCOME/GROWTH PROGRAM SIX-B, L.P.

                     NOTES TO CONDENSED FINANCIAL STATEMENTS
                                   (CONCLUDED)

                    ========================================

3.       EARNINGS PER UNIT OF LIMITED PARTNERSHIP INTEREST

         Earnings and losses per unit of limited partnership interest is based
on the average number of units outstanding during the periods presented. For
this purpose, earnings and losses are allocated 99% to the limited partners and
1% to the general partners.

4.       RECLASSIFICATIONS

         Certain 1996 amounts have been reclassified to conform to the 1997
presentation.



                                      -6-

<PAGE>   7
                    ENSTAR INCOME/GROWTH PROGRAM SIX-B, L.P.


ITEM 2.  MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND RESULTS
         OF OPERATIONS

INTRODUCTION

         On February 8, 1996, President Clinton signed into law the
Telecommunications Act of 1996 (the "1996 Telecom Act"). This statute
substantially changed the competitive and regulatory environment for
telecommunications providers by significantly amending the Communications Act of
1934, including certain of the rate regulation provisions previously imposed by
the Cable Television Consumer Protection and Competition Act of 1992 (the "1992
Cable Act"). Compliance with those rate regulations has had a negative impact on
the Partnership's revenues and cash flow. The 1996 Telecom Act provides that
certain of the rate regulations will be phased out altogether in 1999. Further,
the regulatory environment will continue to change pending, among other things,
the outcome of legal challenges and FCC rulemaking and enforcement activity in
respect of the 1992 Cable Act and the 1996 Telecom Act. There can be no
assurance as to what, if any, further action may be taken by the FCC, Congress
or any other regulatory authority or court, or the effect thereof on the
Partnership's business. Accordingly, the Partnership's historical financial
results as described below are not necessarily indicative of future performance.

         This Report includes certain forward looking statements regarding,
among other things, future results of operations, regulatory requirements,
competition, capital needs and general business conditions applicable to the
Partnership. Such forward looking statements involve risks and uncertainties
including, without limitation, the uncertainty of legislative and regulatory
changes and the rapid developments in the competitive environment facing cable
television operators such as the Partnership. In addition to the information
provided herein, reference is made to the Partnership's Annual Report on Form
10-K for the year ended December 31, 1996 for additional information regarding
such matters and the effect thereof on the Partnership's business.

RESULTS OF OPERATIONS

         The Partnership's revenues increased from $575,200 to $730,800, or by
27.1%, for the quarter ended March 31, 1997 as compared to the corresponding
period in 1996. Of the $155,600 increase, $69,900 was due to increases in
regulated service rates that were implemented by the Partnership in the second
and fourth quarters of 1996, $46,300 was due to increases in the number of
subscriptions for basic and premium services, $24,500 was due to increases in
other revenue producing items consisting primarily of advertising sales revenue
and incentive fees from programmers, and $14,900 was due to the restructuring of
The Disney Channel from a premium channel to a tier channel effective July 1,
1996. As of March 31, 1997, the Partnership had approximately 7,200 homes
subscribing to cable service and 2,100 premium service units.

         Service costs increased from $189,100 to $240,100, or by 27.0%, for the
quarter ended March 31, 1997 as compared to the corresponding period in 1996.
Service costs represent costs directly attributable to providing cable services
to customers. Of the $51,000 increase, $28,900 related to increases in
programming fees (including primary satellite fees), $10,800 was due to an
increase in franchise fees and $4,100 was due to a decrease in capitalization of
labor and overhead expense due to fewer capital projects in the first quarter of
1997. The increase in programming fees during the three months ended March 31,
1997 was due to higher rates charged by programming suppliers, increases in the
number of subscriptions for services and a $5,100 increase related to the
restructuring of The Disney Channel discussed above.


                                      -7-
<PAGE>   8
                    ENSTAR INCOME/GROWTH PROGRAM SIX-B, L.P.

RESULTS OF OPERATIONS (CONCLUDED)

         General and administrative expenses increased from $97,900 to $100,100,
or by 2.2%, for the quarter ended March 31, 1997 as compared to the
corresponding period in 1996. Of the $2,200 increase, $2,700 was due to an
increase in personnel costs and $1,900 was due to an increase in advertising
sales expense. These increases were partially offset by a $2,000 decrease in
insurance premiums.

         Management fees and reimbursed expenses increased from $54,200 to
$66,300, or by 22.3%, for the quarter ended March 31, 1997 as compared to the
corresponding period in 1996. Of the $12,100 increase, management fees increased
by $7,800 in direct relation to increased revenues as described above and
reimbursed expenses increased by $4,300, primarily due to higher allocated
personnel costs, professional fees and telephone expense.

         Depreciation and amortization expense increased from $211,600 to
$271,200, or by 28.2%, for the quarter ended March 31, 1997 as compared to the
corresponding period in 1996 primarily due to a reduction in the estimated
remaining life of existing plant, which is scheduled to be rebuilt in 1998 and
1999.

         Operating income increased from $22,400 to $53,100 for the quarter
ended March 31, 1997 as compared to the corresponding period in 1996 primarily
due to increases in revenues as described above.

         Interest expense, net of interest income, decreased from $37,900 to
$31,000, or by 18.2%, for the quarter ended March 31, 1997 as compared to the
corresponding period in 1996, primarily due to a decrease in average borrowings
to $1,288,400 during the quarter ended March 31, 1997 from $1,630,700 during the
corresponding period in 1996.

         Due to the factors described above, the Partnership generated net
income of $22,100 for the quarter ended March 31, 1997 compared to a net loss of
$15,500 for the corresponding period in 1996.

LIQUIDITY AND CAPITAL RESOURCES

         The Partnership's primary objective, having invested its net offering
proceeds in cable systems, is to distribute to its partners all available cash
flow from operations and proceeds from the sale of cable systems, if any, after
providing for expenses, debt service and capital requirements relating to the
expansion, improvement and upgrade of its cable systems. The Partnership
currently relies exclusively on the availability of cash generated from
operations to fund its ongoing expenses, debt service and capital requirements.
In general, these requirements involve expansion, improvement and upgrade of the
Partnership's existing cable systems. As of the date of this Report,
substantially all of the available channel capacity in the Partnership's systems
is being utilized and each of such systems requires rebuilding. The desired
rebuild program is presently estimated to require aggregate capital expenditures
of approximately $7.2 million, although the majority of the total is not planned
to be spent until 1998 and 1999. These rebuilds cover seven franchise areas in
Georgia and are required by two existing franchise agreements. The cost to
rebuild the two franchise areas is estimated to be approximately $1.8 million
and must be completed by February 1999. Two of the remaining five franchise
agreements are under negotiation for renewal. The Partnership's management
believes that the Partnership's cash flow and other sources of capital will be
adequate to meet its current liquidity requirements, which include necessary
capital expenditures of


                                      -8-
<PAGE>   9
                    ENSTAR INCOME/GROWTH PROGRAM SIX-B, L.P.

LIQUIDITY AND CAPITAL RESOURCES (CONTINUED)

approximately $687,000 in 1997, $223,000 of which is to extend the Partnership's
systems to pass new serviceable homes in their franchise areas. To incur this
level of capital expenditures, however, the Partnership will be required to
continue to defer the payment of a portion of its previously deferred management
fees. As of March 31, 1997, the Partnership owed the Corporate General Partner
$659,100 for deferred management fees and reimbursable expenses, and also owed
an affiliate in excess of $318,000 for programming fees. Failure to rebuild the
cable systems in a timely fashion could have a material adverse effect on the
value of those systems compared to systems that have been rebuilt to a higher
technical standard. The Partnership's term loan agreement restricts capital
expenditures to $700,000 in 1996 and thereafter. Funding rebuild capital
expenditures beyond 1997 will, therefore, most likely require refinancing of the
Partnership's credit arrangements, and there can be no assurance that the
Partnership will be able to obtain such a refinancing on terms acceptable to the
Partnership. Refinancing will be required in order for the Partnership to
perform substantially all of its planned rebuild construction, although
refinancing alone may still not permit all the rebuilds to be completed due to
limitations on indebtedness imposed by the partnership agreement, which is
discussed below.

         As previously disclosed, in response to the FCC's amended rate
regulation rules and the Partnership's capital expenditure requirements,
distributions to Unitholders were discontinued in July 1994. As stated at the
time of the announcement of this decision, management believes that it is
critical for the Partnership to preserve its liquidity though the retention of
cash. As a result, and because of the pending rebuild requirements discussed
above, the Partnership does not anticipate paying distributions at any time in
the foreseeable future.

         On March 31, 1997, the outstanding balance of the Partnership's term
loan was $1,288,400 and is payable in quarterly installments ranging from
$105,700 to $161,000, plus interest. The term loan agreement requires principal
payments of $422,800 in 1997, $543,600 in 1998 and $322,000 in 1999. The
Partnership made its first scheduled 1997 principal repayment on April 9, 1997,
which reduced its outstanding borrowings to $1,182,750.

         The Partnership's term loan agreement contains certain financial tests
and other covenants including, among others, restrictions relating to
acquisitions of cable systems and capital expenditures. The Partnership believes
that it was in compliance with its debt covenants as of March 31, 1997.

         The partnership agreement provides that without the approval of a
majority of interests of limited partners, the Partnership may not incur any
borrowings unless the amount of such borrowings together with all outstanding
borrowings does not exceed 33% of the original capital raised by the
Partnership, or a maximum of $3,052,500 permitted debt outstanding. As discussed
above, in order to obtain the appropriate amount of capital to rebuild and
upgrade the Partnership's systems, this provision of the partnership agreement
would need to be amended to increase the Partnership's leverage. There can be no
assurance that the Partnership will be able to effect such an amendment to the
partnership agreement.


                                      -9-
<PAGE>   10
                    ENSTAR INCOME/GROWTH PROGRAM SIX-B, L.P.

LIQUIDITY AND CAPITAL RESOURCES (CONCLUDED)

         THREE MONTHS ENDED MARCH 31, 1997 AND 1996

         Cash provided by operating activities increased by $346,000 from
$223,800 for the three months ended March 31, 1996 to $569,800 for the three
months ended March 31, 1997. This increase was primarily due to a $234,600
reduction in receivable balances that resulted, in part, from an insurance
settlement for storm damage to the Partnership's Georgia cable systems.
Partnership operations generated $97,700 more cash in the 1997 quarter after
adding back non-cash depreciation and amortization charges. The Partnership used
$18,500 less cash for prepaid expenses and accounts payable due to differences
in the timing of payments.

         The Partnership used $93,600 more cash in investing activities during
the three months ended March 31, 1997 than in the comparable three months of
1996 due to an increase of $97,400 in expenditures for tangible assets partially
offset by a decrease of $3,700 in expenditures for intangible assets. Financing
activities used $702,200 more cash in the first three months of 1997 than in the
comparable 1996 quarter due to the payment of previously deferred amounts owed
to the Corporate General Partner.

         Operating income before depreciation and amortization (EBITDA) as a
percentage of revenue increased from 40.7% to 44.4% during the first three
months of 1997 compared to the corresponding 1996 period. The change was
primarily due to increased revenue. EBITDA increased from $234,000 to $324,300,
or by 38.6%, for the three months ended March 31, 1997 as compared to the first
three months of 1996.

INFLATION

         Certain of the Partnership's expenses, such as those for equipment
repair and replacement, billing and marketing generally increase with inflation.
However, the Partnership does not believe that its financial results have been,
or will be, adversely affected by inflation in a material way.


                                      -10-

<PAGE>   11
                    ENSTAR INCOME/GROWTH PROGRAM SIX-B, L.P.


PART II.          OTHER INFORMATION


ITEMS 1-5.        Not applicable.

ITEM 6.           Exhibits and Reports on Form 8-K

                  (a)      None

                  (b)      No reports on Form 8-K were filed for the quarter for
                           which this report is filed.



<PAGE>   12
                                   SIGNATURES


Pursuant to the requirements of the Securities Exchange Act of 1934, the
Registrant has duly caused this report to be signed on its behalf by the
undersigned thereunto duly authorized.





                    ENSTAR INCOME/GROWTH PROGRAM SIX-B, L.P.

                          a GEORGIA LIMITED PARTNERSHIP
                          -----------------------------
                                  (Registrant)



                                     By:  ENSTAR COMMUNICATIONS CORPORATION
                                          General Partner






Date:  May 6, 1997                   By:  /s/ Michael K. Menerey
                                          -------------------------
                                          Michael K. Menerey,
                                          Chief Financial Officer