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$ \sum \limits_{n \in \mathbb{N}} \frac{1}{n^{3}}$

Is there a way to sum this sequence analytically?

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    This is sorta the [second half of this question](http://math.stackexchange.com/questions/107345/zeta-of-three-question-about-closed-form/107348#107348). There are other MSE questions floating around related to this one, like its irrationality and relation to powers of $\pi$.2012-02-20

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No one has ever found a closed form for this number, and it hasn't been for lack of trying. All the "obvious" possibilities (e.g., $p\pi^3/q$ for reasonable sized integers $p$ and $q$) have been ruled out.