How would i prove that cuberoot 2 is not rational?

Let cuberoot 2 be written in the form m/n, where m and n are coprime.

So then

Hence and thus m is divisible by 2

So there exists integer k such that m=2k

thus =

Thus =

Where do i go next? im stuck. Does it matter that its 4k^3 instead of say 2k^3? Can i just say that n^3 is thus even?