(n+1)³-n³=3n²+3n+1n³-(n-1)³=3(n-1)²+3(n+1)+1……2³-1³=3*1²+3*1+1全都加起来左边正负抵消(n+1)³-1³=3*(1²+2²+……+n²)+3*(1+2+……+n)+1*n1+2+……+n=n(n+1)/2则(n+1)³-1=3*(1²+2²+……+n²)+3n(n+1)/2+n整理得1²+2²+……+n²=n(n+1)(2n+1)/6
