Volume of sphere: V(s) = 4/3*pi*R^3 = (4/3)*pi*(D/2)^3 = (1/6) * pi * D^3
Volume of cube: V(c) = s^3
Volume of them is the same, I'm assuming you actually want to know the length of the cubic vertice
So s^3 = (1/6)*pi*D^3 -> s = (1/6 * pi)^1/3 * 6 = (36pi)^1/3