Factor a cubic and transform its roots

Write down the real root of $w^3+8=0$, where $w$ is a complex number.

Hence, find the other roots of $w^3+8=0$ in exact form.

Deduce the roots of $w^4+w^3+8w+8=0$.

Determine the roots of $z$ such that $z^4-iz^3+8iz+8=0$.