There are many variables to be considered. Ears vary in size considerably and violin cases, while roughly standard, also vary.
With all this uncertainty, and without writing an entire thesis complete with confidence intervals, we are going to work with figures that could reasonably be considered “average”.
The average mass of a human ear is approximately 8.4cm cubed. If you require workings they can be supplied.
The average violin case volume is very hard to measure but we are going to go with 830cm cubed. Again, if you require workings they can be supplied!
The answer is therefore 99 ears.
1) Ears (probably) do not tessellate well and therefore there would be a number of air gaps between them which would reduce the number that could fit.
2) Ears however are quite bendy and therefore the issue in point 1 above could probably be offset by, for want of a better phrase, squashing more ears into the case.