So I recently came across this problem:
$\large{x^{3}+ (x+1)^{3}+\cdots\cdots+(x+15)^{3}=y^{3}}$
Find how many ordered pairs for $\large{(x,y)}$ satisfy the above equation. Both $x,y$ are positive integers.
I can do it using computer program but this problem was supposed to be solved by hand and I have no idea how. How can I do it?
EDIT: The other question doesn't have any answer either.