  In this article, we construct the
charmed-diquark-charmed-diquark-charmed-diquark type current to study the
axialvector triply-charmed hexaquark state with the QCD sum rules in details.
In calculations, we take the energy scale formula
$\mu=\sqrt{M^2_{H}-(3{\mathbb{M}}_c)^2}$ to choose the pertinent energy scale
of the QCD spectral density so as to enhance the pole contribution and improve
the convergent behavior of the operator product expansion. If the spin-breaking
effects are small for the triply-charmed hexaquark states, the ground state
hexaquark states with $J^P=0^+$, $1^+$ and $2^+$ are estimated to have the
masses about $5.8\,\rm{GeV}$ and narrow widths.
