Having done a number of 8-12 day trips over the years, I was always comfortable around 4,800 - 5,500 CI's or roughly 80-90 Liter packs.
*Note...I wasn't sure if you were saying no resupply and no tent or no resupply but you needed a tent.
The pack, tent, and sleeping bag are the big three, but the pack will be dependant upon your level of gear integration (that sounds pretty cool).
For instance... I always carried a whisperlite, 22oz fuel bottle and 2 liter steel cooking pots (MSR Cascade set) . Now there is ultralight Pepsi can stoves and much smaller Ti pots, taking up much less room. A Down bag might save you 500-750 cubic inches over a synthetic bag and small 1-person tent or a single wall sylnylon shelter will probably save you 750-1,000 cubic inches over a standard 4.5-5.0 lb 2 person 3 season tent.
Clothing is another space-saver or space taker (depending on how you look at it) I rarely wear hiking pants in the 3 season, preferring shorts and a pair of lightweight rain pants for use on summits and ridges or in wind driven rain, and a pair of running tights for the coldest nights - I do usually wear gaiters. I have 2 sets of clothes, one on and one in the pack. I wear my rain-gear if I stop to do laundry. But plan on much less bulk for summer backpacking.
I carry a 100 weight fleece shirt between June and August, and a 200 weight fleece jacket for April/May September/October.
Food is your biggest weight factor and the nice thing is it will diminish in weight and volume each day, but for 8 days, if you are not into ultralight and latest technology, you would probably have a 40+lb pack.
One thing you don't want is to have a pack that is too small and end up cramming it so full that it bulges, as I find the packs don't ride as well when they are crammed/rammed hard with gear and food.
I put together some info a number of years ago for my former ADK chapter, and later gave it to my AMC Chapter - It might help you
Here
Factors (bulk and pack size can also change depending on where you are heading. A week in the whites or on the LT in May is far different from a week on the AT in the Shenandoah's in May.