Aman's Greek Letter Challenge

Algebra Level 5

Let

λ=13+23+33+.........+ρ3  (1ρ100).\lambda = 1^3+2^3+3^3+.........+\rho^3\ \ (1\leq\rho\leq100).

If the sum of all perfect square values of λ\lambda is ζ,\zeta, what is the value of ζ107?\lfloor\frac{-\zeta}{10^7}\rfloor?

Also try A tribute to Ramanujan

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