  In this article, we construct the color-singlet-color-singlet type currents
and the color-singlet-color-singlet-color-singlet type currents to study the
scalar $D^*\bar{D}^*$, $D^*D^*$ tetraquark molecular states and the vector
$D^*D^*\bar{D}^*$, $D^*D^*D^*$ hexaquark molecular states with the QCD sum
rules in details. In calculations, we choose the pertinent energy scales of the
QCD spectral densities with the energy scale formula
$\mu=\sqrt{M^2_{T}-(2{\mathbb{M}}_c)^2}$ and
$\sqrt{M^2_{H}-(3{\mathbb{M}}_c)^2}$ for the tetraquark and hexaquark molecular
states respectively in a consistent way. We obtain stable QCD sum rules for the
scalar $D^*\bar{D}^*$, $D^*D^*$ tetraquark molecular states and the vector
$D^*D^*\bar{D}^*$ hexaquark molecular state, but cannot obtain stable QCD sum
rules for the vector $D^*D^*D^*$ hexaquark molecular state. The connected
(nonfactorizable) Feynman diagrams at the tree level (or the lowest order) and
their induced diagrams via substituting the quark lines make positive
contributions for the scalar $D^*D^*$ tetraquark molecular state, but make
negative or destructive contributions for the vector $D^*D^*D^*$ hexaquark
molecular state. It is of no use or meaningless to distinguish the factorizable
and nonfactorizable properties of the Feynman diagrams in the color space in
the operator product expansion so as to interpret them in terms of the hadronic
observables, we can only obtain information about the short-distance and
long-distance contributions.
