Consider $n$ points equally spaced around the unit circle, joined by all possible combinations of lines to make a complete graph. Let $g(n)$ be the number of triangles formed in the resulting diagram.

For example, $g(3) = 1$, $g(4) = 8$, $g(5) = 35$, $g(6) = 110$.

What is the general formula for $g(n)$?

You can see my initial progress on this puzzle here.