Can a male cocktail mate with a female parakeet?

i got a parakeet just 1.but next 2 the cage i have a par of cocktail birds.my parakeet had 2eggs in the the cage this mornin....so am thinken maybe the boy cocktail had sex with it throw the gate it sounds funny but i swair this is real....no lie can somebody anser this 4 me whats good....