After moving to Schwerin he studied under Friedrich Lührss, Paul Aron, and George Rettberg.
He learned piano as a child and played chamber music in his youth. He composed the song Ach, wie wärs möglich dann, which became quite popular and resulted in his being chosen for the court of Grand Duke Paul Friedrich von Mecklenburg-Schwerin. He furthered his studies in 1832 with Joseph Birnbach in Berlin and later with Sechter in Vienna (1841-1843), as well as with Halevy and Marco Bordogni in Paris.
He held a conducting position at a Stuttgart court theater from 1851 to 1861.
He died in Schwerin. Nikolai Rimsky-Korsakov viewed Kücken"s work dimly as "saccharine." His most popular work was the opera Der Prätendent, premiered in Stuttgart in 1847.