### Unexpected result for the sum of a series

I typed

```
n = var('n')
sum(1/((2*n-1)^2*(2*n+1)^2*(2*n+3)^2), n, 0, oo)
```

sage answered

```
3/256*pi^2 - 1/32
```

By hand computation (via Fourier series), and by WolframAlpha I got

3/256*pi^2

Why?

Link to WolframAlpha's result.

(This is my first question. If it is inappropriate here, please tell me where I should ask it. I used the tag "bug", but I of course mean "potential bug". Thank you very much in advance!)