Why would a brand new radiator be leaking lots of cooolant and smoke coming from under the hood?

I would start with checking all the hose clamps and hoses to make sure they are properly tightened and not damaged. Also check that the thermostat housing is not leaking along with the water pump. Especially if any of these were replaced when the radiator was replaced. Also check to see if drain cock is closed. Also make sure the overflow hose is correctly routed to the overflow tank. You might just have to run the engine and open the hood and see where the leak is coming from. Good luck.