What is a resaonable estimate for the volume of a number cube: 8 cm 27 in 1 ft?

There's no way to even guess, because you've told us nothing
about the number cube.  We don't know whether it's the size of
a grain of salt or the size of a house.  It would be a major big help
if you told us roughly the approximate length of one of its edges.

The answer to your question is 1/9