I’ve always believed it to have been his 56th birthday, April 20, 1945, but I’ve been finding a lot of other sources that say March 20th instead. Which was it for sure?
In the end, this is a fairly simple matter: While the last German Wochenschau (third episode of Nr. 755), which depicts Hitler and Hitler youth member Alfred Czech is dated and references Hitler's last birthday on April 20, 1945 the scenes were shot either on March 19 or 20. By April 20, 1945 there was already a city--wide prohibition on filming in Berlin due to the Soviet advances in the city. While some witnesses said that on April 20, 1945 Hitler also received some youths near the bunker, no photos or film reels of this exist.
In this sense, what counts as the last public appearance is up to the question what constitutes public: On April 20,1945 an undetermined number of HJ members saw Hitler outside the Reichskanzlei while the German public at large was shown images in the Wochenschau that had been taken a month before.
This is all laid out in more detail in Anne Luise Kiss: Die letzten Filmaufnahmen von Adolf Hitler – Qualitative Dimensionen ihrer Verwendung in Film- und Fernsehdokumentationen, Brandenburg 2013.