  We calculate the next-to-next-to-leading order ${\cal O}(\alpha_s^4)$
one-loop squared corrections to the production of heavy-quark pairs in the
gluon-gluon fusion process. Together with the previously derived results on the
$q \bar{q}$ production channel the results of this paper complete the
calculation of the one-loop squared contributions of the
next-to-next-to-leading order ${\cal O}(\alpha_s^4)$ radiative QCD corrections
to the hadroproduction of heavy flavors. Our results, with the full mass
dependence retained, are presented in a closed and very compact form, in
dimensional regularization.
