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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 $\lfloor\frac{-\zeta}{10^7}\rfloor?$

Also try A tribute to Ramanujan

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