2n(2n+2)
=4n^2+4n
1^2+2^2+3^2+...+n^2=n(n+1)(2n+1)/6
2*4+4*6+6*8+…+2n(2n+2)
=4*1^2+4*1+4*2^2+4*2+4*3^2+4*3+.+4n^2+4n
=4(1^2+2^2+3^2+...+n^2)+4(1+2+3+...+n)
=4*n(n+1)(2n+1)/6+4*(1+n)*n/2
=2n(n+1)(2n+1)/3+2n(n+1)
=2n(n+1)[(2n+1)/3+1]
=2n(n+1)[(2n+1)+3]/3
=2n(n+1)(2n+4)/3
=4n(n+1)(n+2)/3