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

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 $s$