Eccoci.

Consider the number $50$.
${50}^2=2500=2^2\times 5^4$, so $\varphi (2500)=2\times 4\times 5^3=8\times 5^3=2^3\times 5^3$. ¹
So $2500$ is a square and $\varphi (2500)$ is a cube.

Find the sum of all numbers $n$, $1<n<{10}^{10}$ such that $\varphi (n^2)$ is a cube.

¹ $\varphi$ denotes Euler's totient function.