Consider a sphere with a diameter of 12 cm. A cylinder is inscribed inside this sphere in such a way that the diameter of the cylinder is equal to the diameter of the sphere, and the height of the cylinder is also equal to the diameter of the sphere. Calculate the volume of the remaining space between the surface of the sphere and the surface of the cylinder. Use the formula for the volume of a sphere, which is given by $$ V = \frac{4}{3} \pi r^3 $$, and the volume of a cylinder, which is given by $$ V = \pi r^2 h $$.