Sounds like your brother is different than you are. It's OK to be different. Since this concerns you so much I suggest that you talk with him about how you feel.
However, I'd take my thoughts out of the realm of drama first and work on giving your brother unconditional love. Love him even tho he doesn't feel the same way about birthdays that you do. Focus on the good characteristics that he has. Above all try to not take his actions so personally. I doubt that he's doing this on purpose.
How do you know he does this on purpose?
I suggest that if you tell him in a calm and loving manner that it's important to you that he acknowledge the birthdays he will do better at doing it.
I suggest that there are reasons having nothing to do with you that he acknowledges the other children. For one thing, they're older. Perhaps he's spent more time with them and feels closer to them.
Not acknowledging their birthdays does not mean he doesn't care about them. He just has a different relationship with them then he does with the older children.
I like the suggestion that you call him on their birthdays. Make it easy for him to say happy birthday. Make this a win/win situation for both of you. See if you can improve your relationship with him.
Frankly, I might not acknowledge birthdays if the mom gets upset when I miss one. It's off putting to be expected to give. We like to give because we have decided to give. None of us like to be told we have to do such and such to prove our love.
You want to acknowledge birthdays. Sounds like you think it's expected of you and you accept that. That's your choice. Your brother may not feel that he needs to acknowledge birthdays. He may want to live his life differently and this is part of that choice. That choice certainly doesn't mean he doesn't love you or your children. Neither does it mean anything personal. It's a different way of relating than you relate. I suggest that is all it is.
Stop with the drama. Let people live the way they choose to live. Don't expect them to live by your rules. Show love and love will be returned. Probably not in the manner you would like but it's love just the same.