  The fully heavy scalar tetraquarks $T_{\mathrm{4Q}}=QQ\overline{Q}\overline{Q
}$, ($Q=c, b$) are explored in the context of QCD sum rule method. We model $
T_{\mathrm{4Q}}$ as diquark-antidiquark systems composed of pseudoscalar
constituents, and calculate their masses $m^{(\prime)}$ and couplings $
f^{(\prime)}$ within the two-point sum rule approach. Our results $m=(6928 \pm
50)~\mathrm{MeV}$ and $m^{\prime}=(18858 \pm 50)~\mathrm{MeV}$ for masses of
the tetraquarks $T_{\mathrm{4c}}$ and $T_{\mathrm{4b}}$ prove that they can
decay to hidden-flavor heavy mesons. The full width $\Gamma_{ \mathrm{4c}}$ of
the $T_{\mathrm{4c}}$ is evaluated by taking into account the decay channels
$T_{\mathrm{4c}} \to J/\psi J/\psi $, $J/\psi \psi^{\prime}$, $\eta _{c}\eta
_{c}$, $\eta _{c}\eta _{c}(2S)$, $\eta _{c}\chi_{c1}(1P)$, and
$\chi_{c0}\chi_{c0}$. The partial widths of these processes depend on strong
couplings $g_{i}$ at vertices $T_{\mathrm{4c} }J/\psi J/\psi $,
$T_{\mathrm{4c}}J/\psi \psi^{\prime} $ etc., which are computed using the QCD
three-point sum rule method. The decay $T_{\mathrm{4b} } \to \eta_{b}\eta_{b}$
is used to find the width $\Gamma_{\mathrm{4b}}$ of the $T_{\mathrm{4b}}$. The
predictions for $m$ and $\Gamma_{\mathrm{4c} }=(128 \pm 22)~\mathrm{MeV}$ are
compared with parameters of the fully charmed resonances reported by the LHCb,
ATLAS, and CMS Collaborations. Based on this analysis, we interpret the
tetraquark $T_{\mathrm{4c}}$ as a candidate to the resonance $X(6900)$. The
mass $m^{\prime} $ and width $ \Gamma_{\mathrm{4b}}=(94 \pm 28)~\mathrm{MeV}$
of the exotic meson $T_{ \mathrm{4b}}$ can be used in future experimental
investigations of these
