Anyone know how to determine a number is quadratic (perfect square i don't know what it's called ) or note?

for example:

for $\displaystyle $n \in \mathbb{Z}^{+}$$

proof that $\displaystyle $(n-1)^{2}+(n-2)^{2}+n^{2}+(n+1)^{2}+(n+2)^{2}$$

isn't quadratic number