Cadillac Repair: Exhaust in Overflow, blown head gaskets, water coolant

Question
I have a 97 Eldo and it is overheating. I pulled the plugs and they are good...fired with out plugs no water. Removed oil ok no water...coolant no oil...exhaust smell in overflow...car runs great, but drive around the block and it overheats.New thermostat, radiator, water pump. water flows through the block great. Any help would be great.

Answer
Have the engine tested for blown head gaskets via constant air pressure inserted into each spark plug hole with all the spark plugs out and see if the coolant overflows or bubbles appaer in the radiator cap opening.

Could also be a faulty water pump, But do the air test first.