求一般公式并证明

(n^2+1)+(n^2+2)+……+(n+1)^2=n^3+(n+1)^3

证明：
左边是一个等差数列求和，共{（n+1）^2-[(n^2)+1]+1}=2n+1项
左边={（n+1）^2+[(n^2)+1]}*（2n+1）/2=(n^2+1+n)*(2n+1)
=[n^2+(n+1)]*[n+(n+1)]
=n^3+(n+1)(n+n^2)+(n+1)^2
=n^3+n(n+1)^2+(n+1)^2
=n^3+(n+1)^3=右边