The original sentence, "I'll be at work later today," could mean either: I'm not a work right now, but I'll be there later day, OR (I am at work now), but I'm leaving for awhile, and I'll be (back) at work later today. (In the second instance, a lot of people would definitely include the word "back". But some wouldn't!) So you can't necessarily conclude, without context, that the speaker is not at work when he says, "I'll be at work later today."

Hello,the first one. It means : I´ll be at my work place later today.