Answer
All real numbers except $2$.
Work Step by Step
Note that $x^3-8=(x-2)(x^2+2x+4).$
The denominator cannot be $0$.
Hence,
$x-2\ne0$ so $x\ne2$
There is no real number that will make $x^2+2x+4=0$ .
Therefore, the domain of the given function is the set of all real numbers except $2$.
