CNN reports that a spokeswoman for Louisiana State University said Robbins, from Baton Rouge, Louisiana, was on a trip with friends celebrating graduation from high school when he went overboard.
The US Coast Guard used helicopters and ocean sentry crews during the search, which covered more than 840sq km before it was called off on Friday evening.
The family, who travelled to the Bahamas in the week,thanked the Bahamas government, the US Coast Guard, the United Cajun Navy and Congressman Garrett Graves “for everything they have done for us”.
“In this time of grief, we thank our family, friends and wellwishers for granting us the privacy we need to properly remember our son and mourn his loss.”
A GoFundMe page has been set up to fundraise for the Robbins family. The page reads, “Cameron went missing during a boating excursion in the Bahamas directly following his high school graduation from University High in Baton Rouge, LA. This fundraiser is to support the Robbins family for anything they may need during this time.”
As of writing, the page has raised US$13,880 ($23,000) from 118 donations.