For full dates, write 10 June 1921 or June 10, 1921, consistently throughout an article (10 June or June 10 where the year is omitted). Generally, use the month first format for (1) US-related articles, and (2) articles not related to a native English-speaking country that already use the month first format.
Avoid changing a consistently used date format in an article just for reasons of personal preference.
