Does the series converge, sigma (2k)/sqrt(k^3 + 1)?

I put this into excel and its obvious it doesn't converge. What I need to figure out is why. It would seem to me that the denominator is approaching infinity at a much faster rate than the numerator and therefore you would have a sum of infinitely smaller number and that should approach a specific number at some point but everything I can find says it diverges and I need to know why. Thank You.