How long is this street?Number Theory Level 5
Let the houses on a street from left to right are numbered 1 through \(n\) in that order. There is a house on the street situated in such a way that the sum of cubes of house numbers to its left is equal to the sum of cubes of house numbers to its right. If \(1\le n\le 10^7\), give the sum of all possible values of \(n\)?
Assume that if there is no house at any side (left or right), the sum of that side is taken to be 0.
Bonus: What are the solutions for \(n>10^7\)?