Gotcha.
(Or are you weighing the lands only? Doubt they'd be that heavy...)
If as Dick alluded to, you are referring to the mass of the air inside the hole, or what the hole itself weighs, no, I didn't figure that. Though I did think of that before posting, so if you were disappointed that I didn't catch that, yea, I did.
What I did was estimated the removed material, and used a nominal diameter of .240. I figured with a 236/244 hole, 240 would be close enough. The difference from 6mm to 30 cal isn't significant either.
/edit.
In a 6mm barrel, the interior circumference is around .750. Assuming the lands are narrower than the grooves, and using a 60/40 ratio, the lands are about .300 total width. Figure .007 deep, for comparison, take a piece of shim stock .007 x .300 x barrel length, and even at 30 inches, you'd probably better use your powder scale to weigh it. It ain't much.