Kuba was drafted in the 1995 NHL Entry Draft by the Florida Panthers in the 8th round, 192nd overall, after playing with HC Vítkovicejunior team in his native Czech Republic. Upon being drafted, he remained in the Czech Republic for one more season, playing with HC Vítkovice's senior team of the Czech Extraliga. Moving to North America, he played the majority of his four seasons with the Panthers in the minor leagues before being traded to the Calgary Flames for Rocky Thompson on March 16, 2000. Before the 2000–01 season began, Kuba was left unprotected by the Flames for the 2000 NHL Expansion Draft and was claimed by the Minnesota Wild. He played his first full NHL season with the Wild in the subsequent season and recorded 9 goals and 30 points. In 2003, the Wild advanced to the playoff semifinals, defeating division rivals Colorado Avalanche and Vancouver Canucks before falling to the Mighty Ducks of Anaheim in four games. Kuba set career playoff marks, appearing in 18 games and scoring 8 points during Minnesota's run. After five seasons with the Wild, he became an unrestricted free agent and on July 1, 2006, he signed with the Tampa Bay Lightning. He left the Wild as the franchise's all-time leader in scoring among defensemen with 33 goals and 132 points in 357 games. During his time with Minnesota, he was named team captain on two occasions, in November 2001 and November 2005, as part of the Wild's monthly rotating captaincy system. Kuba represented the Wild along with teammate Dwayne Roloson in the 2004 All-Star game. In 2006–07, his first season with Tampa Bay, he recorded a career-high 15 goals, 22 assists and 37 points. On August 29, 2008, Kuba was traded to the Ottawa Senators, along with Alexandre Picard and San Jose's first-round draft pick for defenseman Andrej Meszaros. With Ottawa, Kuba broke an NHL record for defensemen with an assist on October 25, 2008, against the Toronto Maple Leafs, giving him at least one point in each of the team's first eight games of the season. The previous best was set in 1981–82 by Brad Park, who recorded a point in each of the Boston Bruins' first seven games. On July 1, 2012, Kuba returned to his original draft team, the Florida Panthers, signing a two-year contract worth $8 million. In the lockout-shortened 2012–13 season, Kuba was unable to live up to his contract registering 10 points in 44 games for the cellar-dwelling Panthers. On July 3, 2013, Kuba was bought out from the remaining year of his deal with the Panthers.
International play
Kuba played his first game for the national team in 2001, and has played 30 times for the Czech national team Played for the Czech Republic in:
