  Alerted by the recent LHCb discovery of exotic hadrons in the range (6.2 --
6.9) GeV, we present new results for the doubly-hidden scalar heavy $(\bar QQ)
(Q\bar Q)$ charm and beauty molecules using the inverse Laplace transform sum
rule (LSR) within stability criteria and including the Next-to-Leading Order
(NLO) factorized perturbative and $\langle G^3\rangle$ gluon condensate
corrections. We also critically revisit and improve existing Lowest Order (LO)
QCD spectral sum rules (QSSR) estimates of the $({ \bar Q \bar Q})(QQ)$
tetraquarks analogous states. In the example of the anti-scalar-scalar
molecule, we separate explicitly the contributions of the factorized and
non-factorized contributions to LO of perturbative QCD and to the
$\langle\alpha_sG^2\rangle$ gluon condensate contributions in order to disprove
some criticisms on the (mis)uses of the sum rules for four-quark currents. We
also re-emphasize the importance to include PT radiative corrections for heavy
quark sum rules in order to justify the (ad hoc) definition and value of the
heavy quark mass used frequently at LO in the literature. Our LSR results for
tetraquark masses summarized in Table II are compared with the ones from ratio
of moments (MOM) at NLO and results from LSR and ratios of MOM at LO (Table
IV). The LHCb broad structure around (6.2 --6.7) 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 their analogue tetraquark
scalar-scalar, axial-axial and vector-vector lowest mass ground states. The
peak at (6.8--6.9) GeV can be likely due to a $\overline{\chi}_{c0}{\chi}_{c0}$
molecule or/and a pseudoscalar-pseudoscalar tetraquark state. Similar analysis
is done for the scalar beauty states whose masses are found to be above the
$\overline\eta_b\eta_b$ and $\overline\Upsilon(1S)\Upsilon(1S)$ thresholds.
