AoPS Wiki talk:Problem of the Day/June 17, 2011

Problem

$\frac{1^{3}+2^{3}+3^{3}+\cdots+x^{3}}{1+2+3+\cdots+x}=\frac{(1+2+3+\cdots+x)^2}{1+2+3+\cdots+x}=1+2+3+\cdots+x$

$1+2+3+\cdots+x=\frac{x\cdot(x+1)}{2}$ Subbing in the value of $x$ we get, $\frac{9001\cdot9002}{2}=\boxed{40513501}$