Actually calculating quantities was not my question, nor does this pose the problem. My question was about cross section labels.
The reason is simple, and beyond my comprehension, but it is not us who call the shots. Some authorities and clients, we work with, are not aware of what modern software can do, so they still think plane (2D), not volume. Consequently they want to see sections, areas on sections and then multiply those areas with distance between sections - to get the volumes and quantities, rather old-ish approach? Unfortunately this request from authorities is not quite that uncommon. We calculated volumes and quantities, and this is 2 minute task in Civil 3D, but we need to label it in manner depicted in figure attached.