# Lim x^3= a^3 when x ->a by epsilon-delta definition?

You need to specify that $\delta$ is less than some fixed value, say 1. Then $|x^2+ax+a^2|<|(a+1)^2+a(a+1)+a^2|$, and I'll call the right-hand side M. So if you specify $\delta=\min(1,\frac{\epsilon}{M})$, you should be able to write out the proof with that.