Pi Function

$\begin{aligned} P & = \prod_{n=2}^\infty \frac {n^3-1}{n^3+1} \\ & = \prod_{n=2}^\infty \frac {(n-1)({\color{#3D99F6}n^2+n+1})}{(n+1)(n^2-n+1)} \\ & = \prod_{n=2}^\infty \frac {n-1}{n+1} \cdot \frac {\color{#3D99F6}(n+1)^2-(n+1)+1}{n^2-n+1} \\ & = \frac {\prod_{n=1}^\infty n}{\prod_{n=3}^\infty n} \cdot \frac {\prod_{n=3}^\infty (n^2-n+1)}{\prod_{n=2}^\infty (n^2-n+1)} \\ & = \frac {1\cdot 2 \cdot \prod_{n=3}^\infty n}{\prod_{n=3}^\infty n} \cdot \frac {\prod_{n=3}^\infty (n^2-n+1)}{(2^2-2+1) \prod_{n=3}^\infty (n^2-n+1)} \\ & = \frac 23 \end{aligned}$

$\implies a+b= 2+3 = \boxed{5}$