$\underset{n\to \infty }{\mathop{\lim }}\,\left[ \frac{1}{{{n}^{3}}+1}+\frac{4}{{{n}^{3}}+1}+\frac{9}{{{n}^{3}}+1}+........+\frac{{{n}^{2}}}{{{n}^{3}}+1} \right]=$