There typical mandrel is made from 1/4" diameter rod. There are a few suppliers that specify a different size mandrel, but the 1/4" seems to be the most common.
7mm pens are made using brass tubes that are 1/4" ID. The 7mm bushings slip over the mandrel; when you turn the blank down to the diameter of the bushing, it will provide the material thickness over the 7mm tubing intended by the pen designer. I just measured the OD of a typical 7mm bushing, and hence the OD of the finished pen, at about 8.4mm.
I've made a couple of 8mm pens that use bushings that have an 1/4" ID, and with a stepped OD - a narrow section that I measured about 7.5mm and that slips inside the 8mm tubes supplied in the kits, and stepping up to the OD specified by the pen designer.
I'm not aware of an '8mm mandrel'.