As far as I know there is no "formula" for finding the cube of a number, so here is a good guess algorythm.
Pass the number in "Number", followed by your "Best guess".
Your best guess can be anything (Number div 2) if you have no idea.
function CubedRoot(Number: Integer; BestGuess: Real): Real;
LastGuess : Real;
LastGuess := 0;
G := BestGuess;
while (G*G*G <> Number) and (LastGuess <> G) do begin
LastGuess := G;
G := (2/3) *G + (1/3) * (Number / (G * G));
CubedRoot := G;