Those motors aren't supposed to leak at the block at any time. I would check for a cracked block. It could be a freeze plug leaking or the water pump. Check your oil for antifreeze also.
Will the radiator leak every time or just when you refill it? It may be just seeking it's own level. It could be a cracked head that is pressurising the radiator. Will it overflow without a cap on it? Check for bubbles in the radiator this could confirm a cracked head.
Not very good news but I hope this helps.
Tom
