  For an integer partition $h_1 + \dots + h_n = N$, a 2-realization of this
partition is a latin square of order $N$ with disjoint subsquares of orders
$h_1,\dots,h_n$. The existence of 2-realizations is a partially solved problem
posed by Fuchs. In this paper, we extend Fuchs' problem to $m$-ary quasigroups,
or, equivalently, latin hypercubes. We construct latin cubes for some
partitions with at most two distinct parts and highlight how the new problem is
related to the original.
