如何用数学归纳法证明这个不等式?

证：n=6时,6^3=2166!=7206^3(k+1)k^3-k^3-3k^2-3k-1=k^4-3k^2-3k-1=(k^4-1)-3k(k+1)=(k^2+1)(k+1)(k-1)-3k(k+1)=(k+1)[(k^2+1)(k-1)-3k]=(k+1)(k^3-k^2+k-1-3k)=(k+1)(k^3-k^2-2k-1)=(k+1)(k^3-2k^2+k^2-2k-1)=(k+1)[k^2(k-2)+k(k-2)-1]=(k+1)[k(k-2)(k+1)-1]k≥6 k-2≥4 k+1≥7k(k-2)(k+1)≥6*4*7>1k(k-2)(k+1)-1>0k+1>0(k+1)[k(k-2)(k+1)-1]>0(k+1)!-(k+1)^3>0(k+1)^3