What 2 cubed numbers equals another cubed number?

Answer 1

First of all, the question does not require the numbers to be integers. That being the case, there are an infinite number of solutions. One of them being:

So 23 + 33 = (3√35)3

So, 2, 3 and the cibe root of 35 meet the requirements.

If they do need to be integers, then (-1)3 + (1)3 = 03 is a possible solution.

Finally if x, y and z need to be positive integers then

xn + yn = zn does not have a solution for n>2 according to Fermat's last theorem.