Which real numbers are equal to their cubes?

let the number be x.
since the cube of the number is equal to the number.
$$\begin{gathered} x^3=x \\ x(x^2-1)=0 \\ x(x-1)(x+1)=0 \\ \Rightarrow x=0 or x=1 or x=-1 \end{gathered}$$
therefore the required numbers are 0,-1,1

hope this helps you