if k is any natural numb, then n^3>kn^2 for all sufficent large n.
(1) The original problem says "for all sufficent large n," while your formula says "there exists n."((For all k)( there exists m)( there exists n)(n.n.n > k.m.m.m))
(2) I don't understand why you replaced "n^3 > kn^2" with "n^3 > km^3."
(3) "For all sufficiently large n" means "for all n that exceed a certain lower bound m." That's why I said $\displaystyle \exists m\forall n.\,n>m\to\dots$ (one can also use >= instead of > here).