$\displaystyle\prod _{ n=2 }^{ \infty }{ \frac { { n }^{ 3 }-1 }{ { n }^{ 3 }+1 } }$ The value of the infinite product above can expressed as $\frac{p}{q}$ where $p$ and $q$ are co-prime positive integers. What is the value of $p+q$?

This problem appeared in Putnam - 1977.

This problem is from the set "Olympiads and Contests Around the World -1". You can see the rest of the problems here.

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