You could have a cracked engine block.
Subaru 2.5 liter engine has a problem with head gaskets. If you have not had your head gaskets replaced, that is the first thing I would suspect.
I would recommend the old green antifreeze as the new Dex-cool is garbbage, it contributes to blown intake gaskets and head gaskets.
White smoke is caused by water and or antifreeze entering the cylinder, and the engine trying to burn it with the fuel. The white smoke is steam. There are special gaskets (head gaskets are the primary gaskets) that keep the antifreeze from entering the cylinder area. The cylinder is where the fuel and air mixture are being compressed and burned. Any amount of antifreeze that enters this area will produce a white steam that will be present at the tailpipe area. If white smoke is present, check to see if the proper amount of antifreeze is inside the radiator and the overflow bottle. Also check to see if antifreeze has contaminated the engine oil. You can look at the engine oil dipstick, or look at the under side of the engine oil filler cap. If the oil is contaminated with antifreeze, it will have the appearance of a chocolate milkshake. Do not start the engine if the oil is contaminated with antifreeze, as serious internal engine damage can result. How did antifreeze get in the oil or cylinder in the first place? The engine probably overheated and a head gasket failed due to excessive heat, thus allowing antifreeze to enter the cylinder (Where it is not meant to be).
Cracked cylinder head, blown head gasket, engine block or intake gaskets.
It is supposed to be red (Dexcool), brown means it got burnt when the engine got hot
A Chevy Cavalier can use standard, all-purpose antifreeze, so it's unlikely that the wrong kind was put in. However, if it is not diluted properly and the antifreeze is mixed with more than 50 percent water, the engine can overheat under some circumstances.
Bad gaskets- including a head gasket- would be a likely suspect.
Assuming you already have a complete engine, a deluxe engine rebuild kit would contain rings, bearings, gaskets, oil pump, and timing chain.
There are 2 freeze plugs in the back of the engine block were the flywheel is, They may be leaking. But I would look at the back top corners of the intake manifold real close and run your fingers around the corners and see if you get antifreeze on them. The intake Gaskets are none to leak on Chevy V8 and V6 engines, It is a common problem.
Blown head gasket or a cracked head. Do not drive this car. Serious engine damage will occur.
If it is motor oil in the anti freeze, then it is either a cracked head, cracked engine block, or a head gasket blown. If it is transmission fluid in your antifreeze, then the radiator is leaking from the transmission cooler ----- although usually that would cause antifreeze to be in your transmission fluid.