"August eighth is a Tuesday."
I mean, yeah it's kinda informal and casual but as someone who speaks Japanese very regularly to a high proficiency, I wouldn't mark it wrong. For instance, sometimes if I'm with a friend at a coffee shop or something I would drop the です or だ, but that's really only something you can do with a friend.
The order is important here as it changes the meaning of the sentence.
八月八日は火曜日です = The eighth of August is a Tuesday. This could be said at any time before 8/8 and still be true as it states which day of the week 8/8 is.
火曜日は八月八日です = Tuesday is the eighth of August. This would only be true on any of the previous six days as it states that the date on the upcoming Tuesday is 8/8.
Hope this makes sense.