Let Sn = 1 * 4 + 2 * 7 +. N (3N + 1), then SN=
Sn=1*4+2*7+.n(3n+1)
=3*1²+1+3*2²+2+...+3*n²+n
=3*(1²+2²+...+n²)+(1+2+...+n)
=3*n*(n+1)*(2n+1)/6+n*(n+1)/2
=n*(n+1)²
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