  An incidence of a graph $G$ is a pair $(u,e)$ where $u$ is a vertex of $G$
and $e$ is an edge of $G$ incident with $u$. Two incidences $(u,e)$ and $(v,f)$
of $G$ are adjacent whenever (i) $u=v$, or (ii) $e=f$, or (iii) $uv=e$ or
$uv=f$. An incidence $k$-coloring of $G$ is a mapping from the set of
incidences of $G$ to a set of $k$ colors such that every two adjacent
incidences receive distinct colors. The notion of incidence coloring has been
introduced by Brualdi and Quinn Massey (1993) from a relation to strong edge
coloring, and since then, attracted by many authors. On a list version of
incidence coloring, it was shown by Benmedjdoub et. al. (2017) that every
Hamiltonian cubic graph is incidence 6-choosable. In this paper, we show that
every cubic (loopless) multigraph is incidence 6-choosable. As a direct
consequence, it implies that the list strong chromatic index of a
$(2,3)$-bipartite graph is at most 6, where a (2,3)-bipartite graph is a
bipartite graph such that one partite set has maximum degree at most 2 and the
other partite set has maximum degree at most 3.
