You should be able to calculate them by counting the number of voxels per structure from the 3D reference download. This link should get you started. Even though it is part of the developing mouse brain atlas API, I think it also applies to the main atlas.
This page might also help.
Finally, I put this information together many years ago, so it may or may not still be accurate:
Downloading CCF annotations:
Download and unzip this: http://download.alleninstitute.org/informatics-archive/current-release/mouse_annotation/P56_Mouse_gridAnnotation.zip
To read in these data in R, use the following:
fn2 = (folder where you unzipped grid annotation data)**
annot = readBin(fn2,what="int",n=159326,size=4)"/energy.raw"), what="double",n=159326,size=4)
I think this is the same as the “template” from here: mouse_connectivity