Yes that's fine

I see. Thank you Alex. That's what I need.

Yes you can. That means you stayed up late. And it was late by the time you went to bed. If you mean it was 3 or 4am, you'd say "it was late at night".

So, I can say "It was a late night", can't I?

Are you asking about times like 3am or 4am - because you can say both for it. I think the two are inter-changeable though. In my experience we say late night, in a situation where we haven't gone to bed. Example would be person A: I was up late at night. person B: Oh really. How late ? person A: around 4am. Another example would be But if we say I woke up at 4am, in the early morning. person A: I woke up early this morning. At around 4am