Footage has surfaced showing 18-year-old Cameron Robbins -- who'd just graduated high school in Baton Rouge -- swimming in the open seas at night near Athol Island last week ... where he was on a sunset cruise with a bunch of his peers celebrating their achievement.

Word is Cameron went overboard on his own accord, and not just that -- but, apparently, it was on a dare. In the clip, you can kinda tell his buddies were getting a kick out of it.

That is until he vanished behind the boat and out of view of everyone, who began screaming at him to grab a life preserver that'd been thrown to him -- which was pretty far away, and he didn't end up reaching it. Once he disappeared, everyone began to panic.

Since he went missing, a multi-day search was undertaken by both Bahamian authorities and the U.S. Coast Guard -- but Robbins was never found, and the search has now been called off after several unsuccessful days of scouring the area for any sign of him.

It sounds like Cameron is presumed dead, as the Coast Guard issued a statement saying ... "We offer our sincerest condolences to Cameron Robbins' family and friends." His family flew into the Bahamas last week, and prayer vigils have been held for him for a few days now.

His family has also spoken out ... "The Bahamas government has called off the rescue for Cameron and we are returning to Baton Rouge. We want to thank the Bahamas government, the U.S. 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 well-wishers for granting us the privacy we need to properly remember our son and mourn his loss."