Proof Writing & Problem Solving · Superchallenge problem

Let $S(n) = 1 \cdot 2 + 2 \cdot 3 + 3 \cdot 4 + \cdots + n(n + 1)$. For how many integers $n$ with $1 \le n \le 1000$ is $S(n)$ divisible by $1000$?