Sum 'em Up 2

Algebra Level 4

Let \[\eta =1+\frac 12+\frac 13+\cdots+\frac 1{2016}.\]

And \[\frac{1^2}{1^3}+\frac{1^2+2^2}{1^3+2^3}+\frac{1^2+2^2+3^2}{1^3+2^3+3^3}+\cdots+\frac{1^2+\cdots+2016^2}{1^3+\cdots+2016^3}=\frac 43\eta-\frac k{6051}.\]

Find the value of \(k\).

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