  Properties of doubly charged scalar tetraquarks $bb\overline{c}\overline{c}$
are investigated in the framework of the QCD sum rule method. We model them as
diquark-antidiquark states $X_{\mathrm{1}}$ and $X_{\mathrm{2}}$ built of
axial-vector and pseudoscalar diquarks, respectively. The masses and current
couplings of these particles are computed using the QCD two-point sum rule
method. Results $m_{1}=(12715 \pm 80)~\mathrm{MeV}$ and $m_{2}=(13370 \pm
95)~\mathrm{MeV}$ obtained for the masses of these particles are used to
determine their kinematically allowed decay modes. The full width $\Gamma_{
\mathrm{1}}$ of the state $X_{\mathrm{1}}$ is evaluated by taking into account
its strong decays to mesons $2B_{c}^{-}$, and $2B_{c}^{\ast -}$. The processes
$X_{\mathrm{2}} \to 2B_{c}^{-}$, $2B_{c}^{\ast -}$ and $
B_{c}^{-}B_{c}^{-}(2S)$ are employed to estimate $\Gamma_{\mathrm{2}}$.
Predictions obtained for the full widths $\Gamma_{\mathrm{1}}=(63 \pm 12)~
\mathrm{MeV}$ and $\Gamma_{\mathrm{2}}=(79 \pm 14)~\mathrm{MeV}$ of these
structures and their masses may be utilized in experimental studies of fully
heavy resonances.
