  Motivated by the LHCb-group discovery of exotic hadrons in the range (6.2
$\sim$ 6.9) GeV, we present new results for the masses and couplings of
$0^{++}$ fully heavy $(\bar{Q}Q)(Q\bar{Q})$ molecules and $(QQ)(\overline{QQ})$
tetraquaks states from relativistic QCD Laplace Sum Rule (LSR) within stability
criteria where Next-to-Leading Order (NLO) Factorized (F) Perturbative (PT)
corrections is included. As the Operator Product Expansion (OPE) usually
converges for $d\leqslant 6-8$, we evaluated the QCD spectral functions at
Lowest Order (LO) of PT QCD and up to $\langle G^3 \rangle$. We also emphasize
the importance of PT radiative corrections for heavy quark sum rules in order
to justify the use of the running heavy quark mass value in the analysis. We
compare our predictions in Table 3 with the ones from ratio of Moments (MOM).
The broad structure arround (6.2 $\sim$ 6.9) GeV can be described by the
$\overline{\eta}_c\eta_c$, $\overline{J/\psi}J/\psi$ and
$\overline{\chi}_{c1}\chi_{c1}$ molecules or/and $\overline{S}_c S_c$,
$\overline{A}_c A_c$ and $\overline{V}_c V_c$ tetraquarks lowest mass ground
states. The narrow structure at (6.8 $\sim$ 6.9) GeV if it is a $0^{++}$ state
can be a $\overline{\chi}_{c0}\chi_{c0}$ molecules or/and its analogue
$\overline{P}_c P_c$ tetraquark. The $\overline{\chi}_{c1}\chi_{c1}$ predicted
mass is found to be below the $\chi_{c1}\chi_{c1}$ threshold while for the
beauty states, all of the estimated masses are above the $\eta_b \eta_b$ and
$\Upsilon(1S)\Upsilon(1S)$ threshold.
