Very recently, the LHCb Collaboration observed distinct structures with the $ccbar{c}bar{c}$ in the $J/Psi$-pair mass spectrum. In this work, we construct four scalar ($J^{PC} = 0^{++}$) $[8_c]_{Qbar{Q^prime}}otimes [8_c]_{Q^prime bar{Q}}$ 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 $6.44pm 0.11$ GeV and $6.52pm 0.10$ GeV, and the narrow structure around $6.9$ GeV can be interpreted as the $0^{++}$ octet-octet tetraquark states with masses $6.87pm 0.11$ GeV and $6.96pm 0.11$ 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 $[cbar{c}][bbar{b}]$ and $[cbar{b}] [b bar{c}]$ tetraquark states, which lie in the range of 12.51-12.74 GeV and 12.49-12.81 GeV, respectively.
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