# Two times, Three times, Thirsty and SAY WHEN???

Level pending

In a Cartesian plane, Let $$A$$ be the set of all natural less than $$15$$ such that there exists a triangle with side length $$n,n+1,n+2$$ which all vertices are lattice points.

Let $$B$$ $$=$$ {$$x^3$$ |$$x$$$$\in$$$$A$$ }.

Let $$s$$ the sum of the elements of $$B$$ . Find the first three digits of $$s$$

×