  Although many series exist for $\pi$ and $\pi^2$, very few are known for
$\pi^3$. In this article, we derive, using a trigonometric identity obtained by
Euler, two representations of $\pi^3$ involving infinite sums and the golden
ratio. The methodology can be generalized in order to obtain further series,
relating by the way $\pi^3$ to other mathematical constants.
