Kupke studied clarinet from 1977 to 1981 at the “Hanns Eisler” University of Music in Berlin. From 1981 to 1987, he was the principal clarinetist at the Theater der Stadt Brandenburg, and from 1987 to 1991, he played saxophone and clarinet at the small venue Das Ei at the Berlin Friedrichstadtpalast. Since 1992, he has worked as a freelance studio and theater musician, performing with institutions such as the Deutsches Theater Berlin, Berliner Ensemble, and the Maxim-Gorki-Theater. In 1989, he was a member of the Günter-Heinz-Quartett, and in 1994, he was a guest musician with the band Animato led by Bernhard Kegel. Since 1995, he has performed in a duo with pianist Hannes Zerbe. He was also a member of the band Frigg, led by Bert Wrede, with whom he recorded several albums. In 1998, the album The Clarinet Trio (Leo Records) was released, featuring Kupke (clarinet), Gebhard Ullmann, and Theo Nabicht (bass clarinet). Since the mid-2000s, he has been a member of the Hermann-Keller-Quartett, and since 2011, he has been a member of Hannes Zerbe’s Jazzorchester Berlin. He has also participated in various Ta Lam band projects by Ullmann, including a tribute album to Charles Mingus (2011). He teaches at the Berlin-Kreuzberg Music School.