Quote:
Originally Posted by enzocreti
216=3^2*(182^2331*10^2)
is there any other positive cube that can be written as
a^2*(b^2r*10^2)?
with a and b positive and coprime, r prime?

Since d^3 = d^2 * d, all you are asking is whether d = (b^2  100r) is positive. In other words, for what values of b and r is b^2 > 100r and b is coprime to d..
It should now be obvious that there are an infinite number of solutions. Picking just one pretty much at random, let r =1. In that case b^2 > 100, or b> 10. One such value is 11. Plugging in the numbers, d=121100 = 21.
Indeed 21^3 = 9261 = 441 * (11^2  10 * 1^2).
Why do you post questions which are so trivial to answer with even the slightest amount of thought?