  We propose a simple method to produce quandle cocycles from group cocycles,
as a modification of Inoue-Kabaya chain map. We further show that, in respect
to "universal central extended quandles", the chain map induces an isomorphism
between their third homologies. For example, all Mochizuki's quandle 3-cocycles
are shown to be derived from group cocycles of some non-abelian group. As an
application, we calculate some $\Z$-equivariant parts of the Dijkgraaf-Witten
invariants of some cyclic branched covering spaces, via some cocycle invariant
of links.
