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The kth term, t(k) is given by t(k) = 2k2 + 2k

So the sum of the first n terms is 2*(12+22+32+...+n2) + 2*(1+2+3+...+n)

= 2*n(n+1)(2n+1)/6 + 2*n(n+1)/2

= n(n+1)*(2n+1)/3 + n(n+1)

= n(n+1)*(2n+1+3)/3

= 2*n(n+1)(n+2)/3

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