  We calculate analytically a class of three-loop vacuum diagrams with two
different mass values, one of which is one-third as large as the other, using
the method of Chetyrkin, Misiak, and M\"{u}nz in the dimensional regularization
scheme. All pole terms in \epsilon=4-D (D being the space-time dimensions in a
dimensional regularization scheme) plus finite terms containing the logarithm
of mass are kept in our calculation of each diagram. It is shown that
three-loop effective potential calculated using three-loop integrals obtained
in this paper agrees, in the large-N limit, with the overlap part of
leading-order (in the large-N limit) calculation of Coleman, Jackiw, and
Politzer [Phys. Rev. D {\bf 10}, 2491 (1974)].
