Kocan was born in Trnava and studied at the Academy of Performing Arts, Bratislava, during which time he performed as a student with Bratislava Chamber Opera House. He went on to further studies with Yevgeny Nesterenko at the Vienna Conservatory. He was a member of the Landestheater Linz 2002–06 and of Basle Opera 2006–08, where his roles included Osmin (Die Entführung aus dem Serail), Philip II (Don Carlo), Méphistophélès (Faust) and King (L’Amour des trois oranges). Engagements elsewhere include Sparafucile (Rigoletto), Ferrando (Il trovatore), Ramfis (Aida), Prince Gremin (Eugene Onegin) and Konchak (Prince Igor) for the Metropolitan Opera, New York, Masetto (Don Giovanni), Banquo (Macbeth) and the Grand Inquisitor and Philip II (Don Carlo) for La Scala, Milan, the title role of Mefistofele in Prague, Duke Bluebeard (Duke Bluebeard’s Castle) and Leporello (Don Giovanni) for Opera Vlaanderen, the Commendatore (Don Giovanni), Osmin and Zaccaria (Nabucco) for Bavarian State Opera, Masetto for Berlin State Opera, the title role of Attila for Teatro Municipal, Santiago, Sarastro (Die Zauberflöte) in Cologne and Banquo and Padre Guardiano (La forza del destino) for Vienna State Opera.
Kocan’s concert repertory includes Mozart’s, Dvořák’s and Verdi’s Requiems, Dvořák’s Stabat mater, Biblical Songs and Gypsy Songs, Mahler’s Symphony no.8 and Musorgsky’s Songs and Dances of Death. He regularly appears in concerts and opera galas in the Czech Republic and internationally, and has broadcast on Slovak television.