$G = 2016^2 - 2015^2 + 2014^2 - 2013 ^2 + 2012^2 - 2011^2 +...+ 2^2 - 1^2$
$= (2016^2 - 2015^2) + (2014^2 - 2013 ^2 )+ (2012^2 - 2011^2) +...+ (2^2 - 1^2)$
$=(2016+2015)(2016-2015)+(2014+2013)(2014-2013)+...+(2+1)(2-1)$
$=2016+2015+2014+...+2+1$
$=\frac{2016(2016+1)}2=2033136$