There is no magic way to do this but there are ways if you can either do the calculation or if you are willing to go through a couple regenerations to get the answer back.
If the volume is simple enough and you can do the math, you can use relations to do the math based on geometry information.
For more complex geometry, you can make a more complex model to calculate the negative volume using analysis. in this case, you actually have to make a "volume" part and subtract your actual part and let analysis return the volume of the "negative" part.
You can use values across parts but your head will swim before you get it all worked out. Watch out for circular references.