Elsewhere I heard that male Long-tailed Tits will care the offspring of their brother if they're unable to have their own. However, I'd like to know if there is a case of such behavior where the two are unrelated to one another.
Yes most commonly in a reciprocal altruism fashion, when you aid any offspring of your species or any in your herd/pack. Crocodiles are known for this. They respond to any crocodile (of their species) distress call from any baby crocodiles. This tends to be an advantage because proximity usually means relatedness and even when it doesn't crocodiles are high enough on the food chain the risk to the males is low compared to the time and effort that would be needed to identify the offspring first.
likewise in herd animals it can be an advantage because it ends up with everyone protecting everyone else's offspring but usually has to be paired with some ability to punish freeloaders/cheaters (individuals who don't help protect the offspring).
Of course you also have males who are tricked into it, after all a male does not always know what are its offspring.
You also have males that will help with a current brood to court the mother, or even unrelated females. Basically they are showing off how good a parent they can be, some believe this is what humans are doing. This is seen in some social primates. It might happen in some birds too but I am not sure.