Proof Writing & Problem Solving · Challenge problem

A pile of $10$ stones is split into two piles, then any pile with more than one stone is split again, and so on until every pile has one stone. Each time a pile is split into piles of sizes $a$ and $b$, you score $ab(a + b)$ points. Strong induction shows the total score does not depend on how the splits are made. What is the total?