Okay, I'll have to admit, I don't think I've ever actually come across a published novel with the exact title 'First Love of Royal Prince'. That phrase is screaming Wattpad or some webnovel platform to me, you know? It sounds like one of those classic billionaire/royalty romance premises you see everywhere online. You could probably find a dozen stories with that exact tagline.
If we're talking the general plot template, though, it's almost always the same: a commoner girl (maybe a scholarship student, a journalist, or just a normal employee) somehow catches the eye of the crown prince of some fictional European-esque kingdom. There's a ton of palace intrigue, stuffy traditions, and a mean queen mother or rival noblewoman trying to break them up. The 'first love' angle usually means he's never been in love before, or his previous relationships were arranged/political, so meeting the heroine completely turns his orderly world upside down. It's pure wish-fulfillment fantasy about being chosen for who you are, not your title or wealth. The conflict is always about whether love can overcome duty.
I remember scrolling through a bunch of these on an app once; they all blend together after a while. The ones that stand out usually have a twist, like the prince actually being undercover as a normal guy when they meet, or the girl having a secret identity of her own. But the core is always that fish-out-of-water romance with a side of palace drama. If you're looking for a specific book, you might need the author's name or the platform it's on. That title alone is way too generic to pin down.