$\begin{aligned} \lim _{n \rightarrow \infty} \frac{1}{n^3} \sum_{k=1}^n\left(k^2\right. & x) \\ & =x \lim _{n \rightarrow \infty} \frac{1}{n} \sum_{k=1}^n\left(\frac{k}{n}\right)^2 \\ & =x \int_0^1 x^2 d x=x\left[\frac{x^3}{3}\right]_0^1 \\ & =\frac{x}{3}\end{aligned}$