What is the most effective way to stay up late and study? Simply caffeine?
As someone who's always been a night owl, try this: Go to sleep. Work intensively in the morning, parts of the afternoon, and early evening. Then relax.
Don't cram. It doesn't work, and it's an awful way to pretend to learn. There's an excellent book that goes into detail on this. It's short, and focuses on effective learning: Law School Fast Track.
PS: Yes, I know, many of us stay up late. It's cool, it's fun. I wrote books late at night. (Early in the morning, really.) But still, I have to support the author of Law School Fast Track on this.