  We obtain finite parts (as well as $\epsilon$-pole parts) of massive
three-loop vacuum diagrams with three-point and/or four-point interaction
vertices by reducing them to tetrahedron diagrams with both massive and
massless lines, whose finite parts were given analytically in a recent paper by
Broadhurst. In the procedure of reduction, the method of integration-by-parts
recurrence relations is employed. We use our result to compute the $\bar{\rm
MS}$ effective potential of the massive $\phi^4$ theory.
