There are only four squares that are equal to the sum of three consecutive cubes.
Zero is one of them.
Find the other three.
(In reply to re(2): solutions
a quote from OEIS:
The equation s^2 = 3c^3 + 6c can be transformed using the substitution X = 3c, Y = 3s into Y^2 = X^3 + 18X, a form of the Weierstrass equation of an elliptic curve: Y^2 = X^3 + aX^2 + bX + c, with a = c = 0. We can now use the SAGE program to show that the there are no other integer solutions. - Jaap Spies, May 27 2007