A cube has 6 sides with equal surface area.
Surface area of each side
= 384 cm^2 / 6
= 64 cm^2
Since this is a cube, each side will be a square surface.
Thus, length of cube
= sqrt(surface area of each side)
= sqrt(64 cm^2)
= 8cm
Volume of cube
= length * length * length
= 8cm * 8cm * 8cm
= 512 cm^3