Kasun started playing basketball at a local club in Delnice, before he started playing professionally with KK Zrinjevac in Zagreb. He was part of the 1998-99 Croatian junior team and the Croatian under-21 team in 2000.
After two seasons in the Zagreb club, and winning the Croatian Cup, in 2000 he moved to the Gonzaga University in the NCAA, but was subsequently suspended by the Croatian Basketball Federation for this abrupt move, and spent two seasons on the bench.
In 2002, he was initially selected by the NBA team Los Angeles Clippers in the second round (41st overall) of the 2002 NBA Draft. On June 26, 2002 he was traded by the Clippers to Orlando in exchange for future considerations. Regardless of this, he then moved to Germany to play for the Opel Skyliners from Frankfurt. With them he won the German championship and performed well in the 2003-2004 ULEB Cup.
In 2004, he returned to the US to play for Orlando. In the season 2004/05 he played in 45 games for Orlando and averaged 7.9 minutes per game.