  Photon-pair direct or jet-associated productions are important for relevant
standard model measurement, Higgs and new physics searches at the LHC. The
loop-induced gluon-fusion process gg -> \gamma\gamma g, which although formally
contributes only at the next-to-next-to-leading order to \gamma\gamma j
productions, may get enhanced by the large gluon flux at the LHC. We have
checked and confirmed previous results on gg -> \gamma\gamma, \gamma\gamma g at
one loop, using now the traditional Feynman diagram based approach and taking
into account the quark mass effects, and further updated them for the 7 and 14
TeV LHC with new inputs and settings. We provide the details and results of the
calculations, which involves manipulation of rank-5 pentagon integrals. Our
results show that the gluon-fusion process can contribute about 10% of the Born
result, especially at small M_{\gamma\gamma} and PT_{\gamma\gamma}, and
increase further the overall scale uncertainty. Top quark loop effects are
examined in detail, which shows importance near or above the threshold
M_{\gamma\gamma} \gsim 2m_t.
