(n-1)^3+n^3+(n+1)^3
=(n-1+n+1)^3-3(n-1)(n+1)(n-1+n+1)+n^3 (1,3两项逆用和的立方展开式)
=8n^3-6n(n-1)(n+1)+n^3
=9n^3-6(n-1)n(n+1)
显然9n^3和6(n-1)n(n+1)都能被3n整除
那么和也能被3n整除