How find this $\prod_{n=2}^{\infty}\left(1-\frac{1}{n^6}\right)$ How find this 
$$\prod_{n=2}^{\infty}\left(1-\dfrac{1}{n^6}\right)$$
I think we can find this value have closed form
$$\prod_{n=2}^{\infty}\left(1-\dfrac{1}{n^{2k}}\right)$$
since
$$1-\dfrac{1}{n^6}=\left(1-\dfrac{1}{n^3}\right)\left(1+\dfrac{1}{n^3}\right)$$
so I think we must find this
$$\prod_{n=2}^{\infty}\left(1-\dfrac{1}{n^3}\right)$$
and
$$\prod_{n=2}^{\infty}\left(1+\dfrac{1}{n^3}\right)$$
Thank you 

As Mhenni Benghorbal mentioned, there is a similar problem which has been treated yesterday and I shall use a similar approach to the one he proposed.  
$$\prod_{n=2}^{m}\left(1-\dfrac{1}{n^3}\right)=\frac{\cosh \left(\frac{\sqrt{3} \pi }{2}\right) \Gamma \left(m-\frac{i
   \sqrt{3}}{2}+\frac{3}{2}\right) \Gamma \left(m+\frac{i
   \sqrt{3}}{2}+\frac{3}{2}\right)}{3 \pi  m^3 \Gamma (m)^2}$$
and
$$\prod_{n=2}^{m}\left(1+\dfrac{1}{n^3}\right)=\frac{(m+1) \cosh \left(\frac{\sqrt{3} \pi }{2}\right) \Gamma \left(m-\frac{i
   \sqrt{3}}{2}+\frac{1}{2}\right) \Gamma \left(m+\frac{i
   \sqrt{3}}{2}+\frac{1}{2}\right)}{2 \pi  \Gamma (m+1)^2}$$ So, the product, from $n=2$ to $n=m$, write $$\frac{(m+1) \cosh ^2\left(\frac{\sqrt{3} \pi }{2}\right) \Gamma \left(m-\frac{i
   \sqrt{3}}{2}+\frac{1}{2}\right) \Gamma \left(m-\frac{i
   \sqrt{3}}{2}+\frac{3}{2}\right) \Gamma \left(m+\frac{i
   \sqrt{3}}{2}+\frac{1}{2}\right) \Gamma \left(m+\frac{i
   \sqrt{3}}{2}+\frac{3}{2}\right)}{6 \pi ^2 m^5 \Gamma (m)^4}$$ If $m$ goes to infinity, the limit is then $$\frac{1+\cosh \left(\sqrt{3} \pi \right)}{12 \pi ^2} =\dfrac{\cosh^2\left(\pi\dfrac{\sqrt3}2\right)}{6\pi^2}$$ as shown by Lucian.
