Listen to My Baby Just Cares for Me online. My Baby Just Cares for Me is an Unknown language song and is sung by Liz Heater. My Baby Just Cares for Me, from the album Oldies but Goodies 60S 70S 80S 90S: Best Old Love Songs & Romantic Music, was released in the year 2021. The duration of the song is 2:30. Download Unknown songs online from JioSaavn.