根据 (n+1)^3-n^3=3n^2+3n+1
2^3-1+3^3-2^3+……+(n+1)^3-n^3=3(1²+2²+3²+.+n²)+3(1+2+3+……+n)+n
-1+(n+1)^3=3(1²+2²+3²+.+n²)+3*(1+n)*n/2+n
化简得 1²+2²+3²+.+n²=n(n+1)(2n+1)/6