Gladio (at some point pre-canon when he's 18 or older) is blatantly flirting with Cor whenever they're alone, putting in all his charm, making obvious innuendos, even touching him when he can get away with it during practice. Cor tries to convince himself he's a reasonable man and none of this affects him. It would be a terrible idea, after all. Gladio's so much younger, Cor is his superior in the Crownsguard, Clarus would strangle Cor if he found out, etc., there are a thousands reasons not to do it, basically. Except, even Cor the Immortal is just a human in the end and eventually he folds and fucks Gladio until he's turned his cocky young admirer into an incoherent, babbling mess.