The 1st term of a sequence of positive integers is $2$; the second term is $6$; the third term is $12$; and the fourth term is $20$. The sequence continues in this manner with the positive difference between successive terms increasing by $2$ each time.The $(n+1)$ term of these sequence can be expressed as $kn^3+pn^2+wn+q$ where $k,p,w,q$ are integers.
How could I find the sum of $k,p,w,q$? I know for a fact that the answer is 6. However I am unsure of the process.