the first of June

June the first

on June 1st.

都可以讲，一般最后一个用的比较多，用了介词on，第一个一般用在句首。给你几个例句：

1.Children' s Day is always the first of June.

2.June the first is International Children's Day.

3.Children's Day in China is on June Ist.

都表示六月一日是儿童节的意思

希望对你有帮助。