Ah you beat me to the Wikipedia answer... cuz.. you know.. it knows everything.

I had no idea about the 'Father' phrase, but I know the 'Daddy' phrase as a kind of "I'm so awesome/I just did/am doing such an awesome job" which usually comes with the expectation of having the answer provided even though it's mostly rhetorical (ie I know I'm your Daddy, but I just want to hear you say it)