  T. Mochizuki determined all 3-cocycles of the third quandle cohomologies of
Alexander quandles on finite fields. We show that all the 3-cocycles, except
those of 2-cocycle forms, are derived from group 3-cocycles of a meta-abelian
group. Further, the quandle cocycle invariant of a link using Mochizuki's
3-cocycle is equivalent to a $\Z$-equivariant part of the Dijkgraaf-Witten
invariant of a cyclic covering of $S^3$ branched over the link using the group.
We compute some Massey triple products via the former invariant.
