\( (z + \frac{8}{3})^3 = z^3 + 3\cdot\frac{8}{3}z^2 + 3\cdot\frac{64}{9}z + \frac{512}{27} = z^3 + 8z^2 + \frac{192}{9}z + \frac{512}{27} = z^3 + 8z^2 + \frac{64}{3}z + \frac{512}{27} \)