By "burns" do you mean there's blue smoke coming out of the tailpipe?
It is not uncommon for an old V8 to allow excess oil past the exhaust valve seals, which then vapourizes in the exhaust system. This is a relatively simple fix -- remove the rocker covers and plugs, hold the valves up with compressed air, remove the rockers, release the collets, replace the seals and reassemble. Allow most of a day if you have never done it before. Special tools are a valve spring compressor, an adapter to apply air pressure through the spark plug hole, and a sleeve to protect the new seals as they pass over the stems. And a magnetic pick-up tool for when (not if) you drop a collet.
Less common, but also possible are worn intake valve seals. They are not subjected to as much heat so they don't harden as bad. If they leak, then the oil actually is burnt, since it is sucked into the intake flow. Typically this will foul plugs or at least cause a significant increase in engine knock compensation.
Least common is excessive oil left by the oil control ring(s). Broken or stuck rings, worn cylinders or excessive big end bearing clearances are the most common causes. Can be fixed, but like Fred said, cheaper and easier to just fit a good used engine.