Series representations for $π^3$ involving the golden ratio

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

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