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

Also try A tribute to Ramanujan

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