Music mogul Simon Cowell has nurtured British boy band One Direction into the spotlight, but members of the band don't seem entirely satisfied Cowell's contribution to their newfound fame and fortune: They say he owes them a trip to Barbados.

After Cowell celebrated his 52nd birthday last week, asked One Direction, who Cowell discovered on the U.K. version of 'The X Factor,' whether they would be giving their mentor a birthday gift. Bandmate Harry Styles said they were waiting to see whether Cowell would deliver on his initial promise to them: "We didn't get Simon anything," he said. "He said he was going to take us to Barbados but he hasn't yet. It would look bad if he made a promise and doesn't come through."

It wouldn't be the first time Cowell made a commitment he couldn't keep — as Cheryl Cole learned the hard way last June after she was unceremoniously axed as a judge from the U.S. reboot of 'The X Factor.' Hopefully Cowell's relationship with One Direction will fare better than his friendship with Cheryl, which soured following her departure from the show.

One Direction's debut single, 'What Makes You Beautiful,' co-penned by 'X Factor' vocal coach Savan Kotecha, skyrocketed to No. 1 on the U.K. Singles Chart in September. We're crossing our fingers for a stateside launch for the boy band, who are set to tour the U.K. in Dec. 2011.