1999 OIM Problems/Problem 1

Problem

Find all positive integers that are less than 1000 and satisfy the following condition: the cube of the sum of their digits is equal to the square of that integer.

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

Solution

This problem needs a solution. If you have a solution for it, please help us out by adding it.

See also

https://www.oma.org.ar/enunciados/ibe14.htm