Yes, this cruise will depart from Rome, Italy, and visiting multiple countries along the way meaning you will need a passport.
If you do not have a passport, it takes several weeks to process, so you'll want to apply sooner rather than later. If you already have a passport, make sure it is not within 6 months of expiration from October 3, 2027 or whenever you choose to return home. If it is, you will need to reapply.