T= r x F
that means torque is exerted at a distance r from center of mass of object. It would depend on where the weight bolt was located in relation to the center of mass of the cue. You can actually ADD weight to the cue, and still not have it change its balance point, it would just have to be closer to center.
If your weight bolt is close to the end of the butt, and it is removed the balance point would be moved forward considerably. However, if it is closer to center, it won't really change much at all.
Most cues do not allow your weight bolt to go deep into the butt, so your weight bolt being removed will most likely move your balance point forward (as stated previously).
Finding the exact center of mass involves triple integrals, so I am guessing giving you that formula wouldn't help much.