Question 3
Let $m$ be a positive integer such that $m^3$ can be expressed as a sum of $m$ consecutive odd integers. For instance, $2^3=3+5$, $3^3=7+9+11$ and $4^3=13+15+17+19$. If 999 is one of the consecutive odd integers in the expression for $m^3$, what is the value of $m$?