Question

Find two natural numbers, such that the difference of their squares is cube and the difference of their cubes is a square. What is the answer in the smallest possible numbers?

Answer 1

let those two numbers be x and y then,
a^3 = x^2 - y^2
and b^2 = x^3-y^3
where a and b must be any integer

Answer 2

If x and y have to be positive, then x=y=1 will do the trick.