The song, which David Beggan wrote, is called Caden's song (My First Christmas).
Proceeds will go to the Yorkhill Children's Foundation, which has a tribute fund in Caden's memory.
Caden's battle with his illness was followed by more than 50,000 people on Facebook until his death on November 20.
On the record, Mr Beggan is joined by Union State, Scottish singer-songwriter JJ Gilmour, formerly of The Silencers, Graeme Duffin, guitarist with Wet Wet Wet and composer David Lyon.
The single was available yesterday as a download via iTunes and Spotify.
Mr Beggan said: "Angela, Declan and Ethan and I are in mourning for Caden and it has been a really difficult time. We miss him more than we can say.
"We wanted to say thank you to Yorkhill hospital and all of the medical teams there especially the 'Blue Angels' who were so compassionate to Caden and ourselves. The purpose of the song is to raise money for the hospital and to leave a memorial for Caden and his struggle.
"We have been so grateful for all of the support and prayers offered on our behalf so far and want to wish everyone who has supported us a happy Christmas and a peaceful new year."
Shona Cardle, chief executive at Yorkhill Children's Foundation said: "In light of the very sad loss of Caden Beggan, we are honoured to have established the Caden Beggan Memorial Fund at Yorkhill Children's Foundation."