A complete search of the internet has found these results:
on August 1st is the most popular phrase on the web.
Both of these constructions are correct but the usage depends on region or country. Note that "August 1st" is usually written as "August 1" but pronounced "August first."
2,483,202 results on the web
Come and see us at the lake on August 1st. It will be a great time for all!
Are you doing anything on August 1st? If not, come and have a party in our yard.
On August 1st, the company will make a big announcement about pricing.
Anything happening on August 1st this year?
What will she be doing on the evening of August 1st?
Where were you on the night of August 1st, Mr. Campbell?
I don't know what this issue with August 1st is all about.
Is the party on August 1st or August 2nd?
533,772 results on the web
You'll look after the tree until the 1st of August.
We won't see each other again until the 1st of August.
I expect you'll come to Warsaw, like every year, on the 1st of August to visit the boys' grave.
It may not be on the 1st of August, it may be January 8th.
Is it usually this hot around here on the 1st of August?
What is she going to do on the 1st of August?
The 1st of August is auspiciously austere and yet audacious.