  Very recently, the LHCb Collaboration observed distinct structures with the
$cc\bar{c}\bar{c}$ in the $J/\Psi$-pair mass spectrum. In this work, we
construct four scalar ($J^{PC} = 0^{++}$) $[8_c]_{Q\bar{Q^\prime}}\otimes
[8_c]_{Q^\prime \bar{Q}}$ type currents to investigate the fully-heavy
tetraquark state $Q Q^\prime \bar{Q} \bar{Q^\prime}$ in the framework of QCD
sum rules, where $Q=c, b$ and $Q^\prime = c, b$. Our results suggest that the
broad structure around 6.2-6.8 GeV can be interpreted as the $0^{++}$
octet-octet tetraquark states with masses $6.44\pm 0.11$ GeV and $6.52\pm 0.10$
GeV, and the narrow structure around $6.9$ GeV can be interpreted as the
$0^{++}$ octet-octet tetraquark states with masses $6.87\pm 0.11$ GeV and
$6.96\pm 0.11$ GeV, respectivley. Extending to the b-quark sector,the masses of
their fully-bottom partners are found to be around 18.38-18.59 GeV.
Additionally, we also analyze the spectra of the $[c\bar{c}][b\bar{b}]$ and
$[c\bar{b}] [b \bar{c}]$ tetraquark states, which lie in the range of
12.51-12.74 GeV and 12.49-12.81 GeV, respectively.
