House Sparrows

I have 2 House Sparrows that I raised. My male, Little Bit is 6 years old and Bambi is 3 years old. On July 1st this year they hatched one egg. The baby is out of the nest and doing well. They are working on another nest now. My question is will the parent birds fight with the baby as it gets older or can they live in the same cage together in harmony. Their cage is 30in x 30in x 18in. Our plans next year when we move is to build an outside home for them all. I can't seem to find anyone that can or will answer my question. Can you?