lim_n → ∞ ((1^2-1)(n-1)+(2^2-2)(n-2)+⋯ ⋯+((n-1)^2-(n-1)) · 1)/((1^3+2^3+⋯ ⋯+n^3)-(1^2+2^2+⋯+n^2)) is equal to:

$\displaystyle \lim _{n \rightarrow \infty} \frac{\left(1^2-1\right)(n-1)+\left(2^2-2\right)(n-2)+\cdots \cdots+\left((n-1)^2-(n-1)\right) \cdot 1}{\left(1^3+2^3+\cdots \cdots+n^3\right)-\left(1^2+2^2+\cdots+n^2\right)}$ is equal to :