\(\lim _{n\to \infty }\frac{\left({1}^{2}-1\right)(n-1)+\left({2}^{2}-2\right)(n-2)+⋯+\left((n-1{)}^{2}-(n-1)\right)\cdo…

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

[JEE Main 2024, 6 Apr (Shift 2)]