We currently have no way to place Volume Quantities on Cross Sections using the Advanced Drafting Tools. I would likely reserve some space on my CrossSection Sheets to place a Table copied from Excel that showed the Section to Section Volumes (extracted from the Corridor Earthwork Report) to provide this requirement today.
We can place Cross Sectional Area information for all materials in the Cross Section, as per the Template Editor - the default templates we gave out at PUG last week show Cut / Fill values, but all materials can be added to that as needed. While not volumes, if your sections are at even stations (e.g. 20' they are relative), but they do not take into account the average of the two end areas of course. This is on my list of enhancements for corridors for future developments.
Alan