As far as I know, it's more common to use the "have been ~ing"-form with for and since. "I've been living in Berlin for six years" feels much more natural to me, if you currently still live in Berlin. "I've lived in Berlin for six years" sounds to me like you do not live there anymore, but there was a period of time when you did. So depends on what you want to say. Hope that helps!

Hello Elena, Your sentence is grammatically correct. If you moved to Berlin 6 years ago and you still live in Berlin, then the sentence has the correct meaning as well. Christine