Geographically Yes. Politically No !
I was born and raised in former West-Berlin, an enclave of Western Germany. Lived in Auckland, New Zealand for 6 months and in Madrid, Spain for 6 months too.
Today, I live in reunified Berlin. In an area that was part of the capital of Eastern Germany: Berlin (East).
Both, the political status of former West-Berlin and East-Berlin ceased to exist after 1990. Its complicated isn't it ?