This is the first song which is performed on The Brady Bunch Hour, sung by The Brady Bunch, which you can hear at the start of the episode.
“Baby Face” is a popular Tin Pan Alley jazz song from 1926, with music by Harry Askt, and lyrics by Benny Davis. The first recording was by Jan Garber and his Orchestra, with Benny Davis signing the chorus only. It was a #1 hit in 1926. The same year, the song was recorded in its entirety by “Whispering” Jack Smith, with Arthur Johnston on piano.
It has been covered numerous times, perhaps most notably by Little Richard, who went to #41 with his version of the song in 1958 – it went to #2 in the UK, his highest-charting single in Britain.