  Productions of multiple gauge bosons at the LHC are sensitive to triple or
quartic gauge couplings and thus provide a sensitive test for the electroweak
sector of the Standard Model and allow for a probe of new physics. In this work
we calculate the gluon-gluon initiate state contribution to the productions of
three gauge bosons ($Z\gamma\gamma$, $ZZ\gamma$ and $W^+W^-\gamma$) at the LHC,
which is formally part of NNLO effects compared to the LO quark-antiquark
channels corrections. For each process we present the ratio between the
gluon-gluon channels contribution and the quark-antiquark channels
contribution. We found that such a ratio for $Z\gamma\gamma$ ($ZZ\gamma$) is of
the order of $10^{-3}$ ($10^{-4}$), much smaller than the corresponding ratio
for the diboson production due to the decrease of gluon PDF when more particles
appear in the final states. These small ratios imply that gluon-gluon fusion
contribution is phenomenological negligible for the productions of
$Z\gamma\gamma$ and $ZZ\gamma$. However, for $W^+W^-\gamma$ production, the
ratio is about 5\%, which is of the same order of magnitude as the ratio for
$W^+W^-$ production due to the big cancellation between the amplitudes of
quark-antiquark channels. While such an effect can be neglected currently at
the LHC, it may be accessible at the HL-LHC.
