This is a good request,
If I were Octavius, there would be three things going through my mind. First, I would be filled with grief over the death of a great man. Julius Caesar was a towering figure in Roman history. He was a great politician, general, and even author. Shakespeare gets at some of these points by showing the favor of the crowds. Moreover, his revealed will showed that he really did love the people.
Second, I would be worried about what to expect next. To be sure, one battle has been finished, but I would be wondering when the next battle would commence. In Act 5 there is an argument between Lepidus and Antony. Anthony comes off very ambitious. In light of this, I would be worrying about Antony's plans.
Finally, I would be worrying about my own future and how I would lead. As you probably know, Octavian at this point was only a teenager.