Putnam Product!

Algebra Level 3

\[\displaystyle\prod _{ n=2 }^{ \infty }{ \frac { { n }^{ 3 }-1 }{ { n }^{ 3 }+1 } } \] 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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