Odd Give, Even Give Unequally...

It is interesting that,

$\cfrac{\pi^2}{6}=\cfrac{1}{1^2}+\cfrac{1}{2^2}+\cfrac{1}{3^2}+...$

and

$\cfrac{\pi^2}{8}=\cfrac{1}{1^2}+\cfrac{1}{3^2}+\cfrac{1}{5^2}+\cfrac{1}{7^2}+...$

but,

$\cfrac{\pi^2}{24}=\cfrac{1}{2^2}+\cfrac{1}{4^2}+\cfrac{1}{6^2}+\cfrac{1}{8^2}+...$

that odd and even numbers do not contribute equally to $\sum^{\infty}_1{\cfrac{1}{n^2}}$

$\cfrac{3}{24}=\cfrac{1}{8}\ne\cfrac{1}{24}$

Odd number contributes three times more than even numbers.

Why?