Volume · Superchallenge problem

A tower is built from $1$-inch cubes in square layers, each one cube thick. The top layer is $1$ cube by $1$ cube, the next layer down is $2$ by $2$, the next is $3$ by $3$, and so on, each layer one cube wider than the one above. The finished tower has a volume of $204$ cubic inches. How many layers does it have?