For two graphs $G_1$ and $G_2$, the {\it Cartesian product} $G_1 \square G_2$ is the graph with vertex set $V(G_1) \times V(G_2)$ in which $(u_1, v_1)$ is adjacent to $(u_2, v_2)$ if and only if $u_1 = u_2$ and $v_1v_2 \in E(G_2)$ or $v_1 = v_2$ and $u_1u_2 \in E(G_1)$. For a nonnegative integer $m$, an {\it $m$-regular graph} is a graph in which every vertex has degree $m$. A {\it factorization} of a graph $G$ is a decomposition of its edge set into edge-disjoint spanning subgraphs called {\it factors}. An {\it $m$-factorization} of a graph $G$ is a factorization of $G$ in which each factor is $m$-regular. A 2-factorization of $G$ in which every factor is a Hamilton cycle is called a {\it Hamilton decomposition} and the graph $G$ is said to be {\it Hamilton decomposable}. An even-order graph $G$ is {\it bipancyclic} if $G$ is a cycle or contains a cycle of every length from 4 to $|V(G)|$, and $G$ is {\it nearly bipancyclic} if it contains a cycle of every length from 4 to $|V(G)|$ except possibly 4 and 8. \par Factorizations of Cartesian products of graphs are a long-standing problem in the literature and have been considered by many authors. For example, J. Aubert and B. Schneider [Discrete Math. {\bf 38} (1982), no.~1, 7--16; MR0676514] showed that the cartesian product of a 4-regular Hamilton decomposable graph with a cycle can be decomposed into three Hamilton cycles, while B.~R. Alspach, J.-C. Bermond and D. Sotteau [in {\it Cycles and rays (Montreal, PQ, 1987)}, 9--18, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 301, Kluwer Acad. Publ., Dordrecht, 1990; MR1096980] showed that the Cartesian product of $n$ cycles of varying lengths is Hamilton decomposable. \par In the paper under review, the authors consider $m$-factorizations of the Cartesian product of even-order Hamilton decomposable graphs such that each factor in the factorization is $m$-connected and bipancyclic or nearly bipancyclic. Extending the results of Aubert and Schneider, through a sequence of lemmas, they show that the Cartesian product of a 4-regular even-order Hamilton decomposable graph $G$ with a cycle has a 3-factorization in which each 3-factor is 3-connected, and if $G$ is bipartite, the factors are isomorphic and nearly bipancyclic. The authors then generalize this result to show that if $G_1$ and $G_2$ are graphs of even orders decomposable into $2n$ and $n$ Hamilton cycles respectively, then $G_1 \square G_2$ has a 3-factorization in which each 3-factor is 3-connected; in addition, if $G_1$ is bipartite, then the factors are isomorphic and nearly bipancyclic. The authors also show that the $n$-cube $Q_n$ has an $m$-factorization in which each $m$-factor is $m$-connected and bipancyclic ($m \not= 3$) or nearly pancyclic ($m=3$) for $m, n \ge 2$ with $m \mid n$.