证明,方法一：(n+1)^4-n^4=4n^3+6n^2+4n+1.∴n^3=(1/4)[(n+1)^4-n^4]-(3/2)n^2-n-1/4∴左边=∑i^3=(1/4)[(n+1)^4-1]-(3/2)*(1/6)n(n+1)(2n+1)-(1/4)n-(n+1)n/2=(1/4)(n^4+4n^3+6n^2+4n-2n^3-3n^2-n-n)-(1/2)(n^2+n)=...