If possible (Carbbed) look into the manifold, Is it reddish in color? If so you have a modulator gone south..Does the smoke smell sickly sweet?
Pull the line from the Carb going down to the Transmission, and plug the carb side..Run the car about a half an hour (in the driveway) Does the smoke dissipate? If so replace the modulator.
Also, If not that, Does the Radiator require constant topping off? Run hot or misfire at any Engine RPM? If so this would indicate a head gasket/Cracked Head/block or bad intake manifold gaskets. Blowing as much smoke as you say, It should be constantly low..and run bad.
Pull the plugs, are any Wet, with water? Crank it while watching the plug holes, do any spray water?
Do a pressure test on the radiator, does it hold pressure..
Try those and let us know