I was going through answers on this [question](https://math.stackexchange.com/questions/656757/evaluating-int-0-infty-fracx3-sin3xx5-dx-using-cont/877629#comment1811019_877629) and came across this [answer](https://math.stackexchange.com/a/784150/38296) and I was wondering how the user arrived at the first line where they state:

$$f(x) \equiv x^3 - \sin^3 x = x^3 + {1 \over 4} \,\sin {3x} - {3 \over 4}\,\sin x$$

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> How does $x^3 - \sin^3 x$ become $x^3 + \frac{1}{4}\sin{3x}-\frac{3}{4}\sin x$?
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Are they using some simple identity or is there some other observation happening?

Thanks!