n²+[n(n+1)]²+(n+1)²
=[(n+1)²-2n(n+1)+n²]+2n(n+1)+[n(n+1)]²
=(n+1-n)²+2n(n+1)+[n(n+1)]²
=1²+2n(n+1)+[n(n+1)]²
=[1+n(n+1)]²