Steve Solkela sings the Happy Birthday song in Finnish: "Paljon onnea vaan." As I understand it, the formal translation of "Happy birthday!" in Finnish is "Hyvää syntymäpäivää!" But "Paljon onnea" or "Paljon onnea vaan" are used more informally to wish someone the best of luck on their big day. That phrase also fits the melody of the song better.
In any case, give Steve Solkela a follow on KZread for more music and Finnish antics: / @stevesolkela