The incident took place in Dunstable Street at about 1.20am on Saturday (January 23) after the pair left Bar 4.
Police are appealing for information about the assault, which was carried out by a group of people.
Investigating officer Detective Constable Claire Case said: “The two men were physically assaulted, causing injuries to both which required hospital treatment, and I’m appealing for anyone who witnessed this to come forward.
“We believe the victims were also involved in a verbal altercation in the bar, so we’d also urge anyone with information about this to get in touch.”
Anyone with information is asked to contact DC Case on 101 or call Crimestoppers, anonymously, on 0800 555 111.