Answer
$$\sum_{i=1}^{n} \sqrt{i+i^{3}}$$
Work Step by Step
Given $$\sqrt{1+1^{3}}+\sqrt{2+2^{3}}+\dots+\sqrt{n+n^{3}}$$
The first term is $ \sqrt{1+1^{3}}$, the last term is $\sqrt{n+n^{3}}$, and we observe that terms are increasing by $1$, so
$$\sqrt{1+1^{3}}+\sqrt{2+2^{3}}+\dots+\sqrt{n+n^{3}}=\sum_{i=1}^{n} \sqrt{i+i^{3}}$$
