  Let $d$ be a fixed positive integer and let $\epsilon>0$. It is shown that
for every sufficiently large $n\geq n_0(d,\epsilon)$, the $d$-dimensional unit
cube can be decomposed into exactly $n$ smaller cubes such that the ratio of
the side length of the largest cube to the side length of the smallest one is
at most $1+\epsilon$. Moreover, for every $n\geq n_0$, there is a decomposition
with the required properties, using cubes of at most $d+2$ different side
lengths. If we drop the condition that the side lengths of the cubes must be
roughly equal, it is sufficient to use cubes of two different sizes.
