Riemann Zeta function of even numbers

[dimension10]

Given that

$$\zeta (2n)=\frac{{\pi}^{2n}}{m}$$

Then how do you find m with respect to n where n is a natural number.

For

n=1, m=6
n=2, m=90
n=3, m=945
n=4, m=9450
n=5, m=93555
n=6, m=$$\frac{638512875}{691}$$
n=7, m=$$\frac{18243225}{2}$$
n=8, m=$$\frac{325641566250}{3617}$$
n=9, m=$$\frac{38979295480125}{43867}$$
n=10, m=$$\frac{1531329465290625}{174611}$$

But I don't see any pattern.

Thanks.

 

[Hurkyl]

I would find it by consulting wikipedia.

 

[dimension10]

Thanks.