If m and n are arbitrary real numbers, then $\displaystyle m^3+n^3$ is not a function of $\displaystyle \sqrt{m}+\sqrt{n}$.
For example, if $\displaystyle m = 11+\sqrt{120}=21.95$ and n = 0, then $\displaystyle m^3+n^3=10582.00$, but if m = 4.95 and n = 6.05, then $\displaystyle m^3+n^3=343.07$.