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The solutions by @CubeyThePenguin is INCORRECT.
I came to bring you the correct solution.
Notice that = 1.077217 cm.
Therefore, there are 435/1.077217 = 403 cubes in one dimension
355/1.077217 = 329 cubes in the other dimension
244/1.077217 = 226 cubes in the third dimension.
So, the final answer is 403*329*226 = 29964662 small cubes.
Solved (correctly).
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By the way, one-line calculation by @Penguin has interior error, which makes his solution nonsensical in degree 2.
TWICE a NONSENSE (!), along and across (!)