## Python, <s>133</s> 129 bytes

    from itertools import*
    n=input()
    l=[];s=0
    for i in range(-n,n+1):l.append(i**2)
    for j in product(l,l):
     if sum(j)==n:s+=1
    print s

This demonstrates the use of itertools cartesian product. [Try it online](http://ideone.com/iq0N9h)