Gwedon Jakoc, 29, from Reading and Tomasz Biernacki, 42, of no fixed address, pleaded guilty to causing GBH in the Aylesbury square.
A third man charged with the same offence, Elias Cordero, 20, of Prebendal Avenue, Aylesbury, appeared at Aylesbury Crown Court on Wednesday but has yet to enter a plea. He is expected to do so on July 3.
Jakoc and Biernacki were arrested at the scene of the May 7 attack, which took place at around 2.30am, while Mr Cordero was arrested later in the day.
The victim was taken to Stoke Mandeville Hospital and discharged two days later after being treated for head injuries.
Kingsbury was cordoned off and roads closed while officers investigated at the scene.