I can only repeat what I have said: find the limit of the arctangent's argument and then find what arctangent is like near that value. You, instead, found the limit of the arctangent's argument divided by $x^3$ and substituted it into arctangent. I don't understand why you divided the argument by $x^3$.
Edit: I just saw your edit, and it is correct. You may also see this discussion on StackExchange for a similar example.