It is possible, but it does take some work.
Simply lube your '06 cases, resize them in the 8x57 sizing die to create a roughly formed, long necked 8mm case. Then trim to length. You likely won't have to turn or ream necks, but you will have to confirm this as you go as to whether they will accept the 8mm bullet and/or fit the loaded rounds into your chamber. Then begin load development which will fireform the cases to your chamber.
The headstamp won't match if it matters to you.
After all that work, you may wonder why you didn't simply buy some 8mm brass. If you need some funds to buy 8mm brass and have lots of .30-06, you could sell the '06 brass on the equipment exchange and then buy the 8mm brass you desire. You might even be able to find someone willing to trade 8mm brass for '06.
