The series of positive integer is grouped into fours as follows :
(1,2,3,4),(5,6,7,8),(9,10,11,12),...
Show that the sum of the integers in the k th bracket is 2(8k-3) .
If you look at the last term in each group, 1st group last term 4, 2nd group last term 8, 3rd group last term 12, we see the kth group would have the last term 4k, thus, the kth group has the numbers $\displaystyle (4k-3,4k-2,4k-1,4k)$. Adding these numbers gives your result.