At the junior youth levels, Kulboka has represented Lithuania on the international stage on several occasions, including at the 2014 FIBA Europe Under-16 Championship and the 2015 FIBA Europe Under-18 Championship. He scored a team-high 15.7 points a game in the 2016 FIBA Europe Under-18 Championship, en route to a silver medal. He also competed for Lithuania in the 2017 FIBA Under-19 Basketball World Cup, averaging a team-high 13.7 points per contest. On 26 February 2018, Kulboka debuted as a member of the senior Lithuanian national team, by scoring nine points, grabbing five rebounds and dishing out two assists, and helped to crush Kosovo's national team, by a score of 106–50, during the 2019 FIBA Basketball World Cup qualification.