I got this from New Scientist magazine. Don't worry, I've already figured it out and it's too late to be sent in for the £15 (it's the first letter opened with the answer in which wins).

In the following statement, digits have been consistently replaced by capital letters, different letters being used for different digits:

DIX is the product of two primes, CENT is a square, MILLE is a cube; none of them starts with a zero.

Which numbers are represented (in this order) by DIX, CENT and MILLE?