There are a couple of versions of this out there...This is a version I found recently and had never heard before, it's cute, but not the one I grew up with.
This is the one I grew up with...
From Dr. Demento.
Both by Lonnie Donegan which was the stage name of Anthony James Donegan (29 April 1931 – 3 November 2002) He was a British singer, songwriter and musician and is revered as the King of Skiffle.
According to Wikipedia:
"Does Your Chewing Gum Lose Its Flavour (On the Bedpost Overnight?)" is a novelty song by Lonnie Donegan. Released as a single in 1959, it peaked at number 3 in the UK Singles Chart. It was also Donegan's greatest chart success in the United States, reaching number five on the Billboard Hot 100 chart in 1961.
The song is a cover version of "Does The Spearmint Lose Its Flavor on the Bedpost Overnight?" written by Billy Rose, Ernest Breuer, and Marty Bloom and first released in 1924 by The Happiness Boys (Ernie Hare and Billy Jones), and later a hit for Lulu Belle and Scotty and The Two Gilberts. The song is humorous in content, the verses each describing a dramatic or urgent scenario leading up to the asking of the titular question.
The title and lyrics of the Donegan version were changed in the UK because "Spearmint" is a registered trademark there, and the BBC would not play songs that mentioned trademarks. Donegan's version of the song was recorded live at the New Theatre Oxford in December 1958 and was released both as a single as a track on the album King of Skiffle. An extended version with more banter was released on the live album The Last Tour.
Since Donegan's version was released, it has appeared as a Smarties jingle, a performance on The Muppet Show, and re-worked into Czech by Jiří Grossmann. Additional versions of the song were recorded by The Irish Rovers and Homer & Jethro. In Ken Kesey's novel One Flew Over the Cuckoo's Nest, the character Randle Patrick McMurphy also sings a few lines of this song to prove Chief Bromden is not deaf by making him laugh at the performance. In 2010, Donegan's version was used as the background song for a satellite TV advertisement for Savlon antiseptic cream. It has also been recorded by Eric Nagler (on his 1982 children's album Fiddle Up a Tune); Ray Stevens covers the song as part of his 9-CD, 108 song box set The Encyclopedia of Recorded Comedy Music (2012).
"Does Your Chewing Gum..." has been a popular song on the Dr. Demento Show, appearing 54 times between the show's premiere and 2006 and selected for the Dr. Demento 20th Anniversary Collection double CD.
It was referenced on Talkin' 'Bout Your Generation.
It was alluded to in the lyrics of "Ahab the Arab" by Ray Stevens.
It has also made an appearance on the children's television show, Sharon, Lois, & Bram's Elephant Show during one of their performances.
"Does The Spearmint..." is sung by the family on HBO's series Boardwalk Empire in season 4 at the end of the episode titled "The Old Ship of Zion."