Date: 202101
Local time of day: 0601-1200
Location: ZZZ.Airport, US
Light: Daylight
Aircraft: Commercial Fixed Wing
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Mission: Passenger
Flight phase: Taxi
ATC / advisory: Tower ZZZ
Reporter organization: Air Carrier
Reporter function: Pilot Not Flying; First Officer
Reporter qualification: Flight Crew Multiengine; Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument
Human factors: Situational Awareness; Distraction; Human-Machine Interface; Confusion; Communication Breakdown
Second reporter function: Captain; Pilot Flying
Anomaly: ATC Issue All Types; Aircraft Equipment Problem Less Severe; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy
Result: Air Traffic Control Provided Assistance; Flight Crew Returned To Clearance
Contributing factors: Environment - Non Weather Related; Human Factors; Software and Automation
Primary problem: Environment - Non Weather Related

Narrative: We pushed from Gate X; after a ATC delay and two CPDLC clearances. At (time) I called Ground frequency to request to taxi. We received clearance to taxi to [Runway] XXL via C. I read it back and we began to taxi. Moments later; while on C; Ground called to inquire what we were doing. I informed them we had just been called and given 'Taxi to XXL via C' and that I read it back. Ground replied that he didn't believe we did. Ground came back and told us to squawk XXXX. We looked down and we had XXXY in there. Turns out our revised CPDLC contained a new routing as well as a new squawk; which we missed. We changed to the correct new code and were told to continue via same taxi route as given originally. No conflict with another aircraft was ever created. We speculated that our wrong squawk created the issue and confused Ground that the aircraft they saw moving wasn't the one they had given the taxi clearance to moments earlier; which was us all along. Probably overkill but we are filling this report simply over Ground's misunderstanding that we had never called for taxi; which we did.


Second narrative: Pushed from Gate X in ZZZ over one hour late because ZZZ1 Center was shut down due to COVID cleaning. We were on our third Release with fuel and routing changes. I was dealing with numerous Passenger and Ops Agent issues.  We started to push for the second time and received notification from Dispatch that we'd received a new Release. I called the jetway back and went to the podium to get the new Release. I asked the FO to check on our clearance. When I got back to the cockpit; we confirmed the new routing; re-briefed the routing and departure; input the new performance data; and ran the Before Push Checklist. We pushed back; started engines and ran the Before Taxi Checklist. The FO asked for taxi and I thought I heard them say for us to taxi to [Runway] XXL via Taxiway Charlie. He read that back; I confirmed the instructions and began to taxi. When we got on Taxiway C; they asked us 'What Company aircraft is on Taxiway Charlie?' We responded with our call sign and shortly thereafter; they asked us to squawk a different code. We'd both missed the fact that our squawk code had changed with the new clearance. We apologized; entered the new code and continue to taxi.


Synopsis: Air carrier flight crew reported communication issues with ATC regarding their taxi to runway clearance.