jmc

Since the volume of a sphere is directly proportional to its diameter cubed, the ratio of the volume of the ball with a diameter of 4 cm to the volume of the ball with a diameter of 3 cm is $(4/3{)}^3=64/27$. Since all of the rubber bands have the same volume, it follows that the number of rubber bands in the ball with diameter 4 is $$(4/3{)}^3\cdot 54=\frac{64}{27}\cdot 54=64\cdot 2=128.$$Therefore the number of rubber bands that Alana needs to add to the ball is $128-54=\boxed{74}$.