Aman's Greek Letter Challenge

Algebra Level 5

Let

$\lambda = 1^3+2^3+3^3+.........+\rho^3\ \ (1\leq\rho\leq100).$

If the sum of all perfect square values of $\lambda$ is $\zeta,$ what is the value of $\lfloor\frac{-\zeta}{10^7}\rfloor?$