JEE Math Practice Question

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

1. A.$$\frac{2}{3}$$
2. B.$$\frac{1}{2}$$
3. C.$$\frac{3}{4}$$
4. D.$$\frac{1}{3}$$