  In this paper, we investigate the spectra of the prospective hidden-bottom
and -charm hexaquark states with quantum numbers $J^{PC }= 0^{++}$, $0^{-+}$,
$1^{++}$ and $1^{--}$ in the framework of QCD sum rules. By constructing
appropriate interpreting currents, the QCD sum rules analyses are performed up
to dimension 12 of the condensates. Results indicate that there exist two
possible baryonium states in $b$-quark sector with masses $11.84 \pm 0.22$ GeV
and $11.72 \pm 0.26$ GeV for $0^{++}$ and $1^{--}$, respectively. The
corresponding hidden-charm partners are found lying respectively at $5.19 \pm
0.24$ GeV and $4.78 \pm 0.23$ GeV. Note that these baryonium states are all
above the dibaryon thresholds, which enables their dominant decay modes could
be measured at BESIII, BELLEII, and LHCb detectors.
