ANSWER:

No, this is not permissible & you must not cut the cake nor be part of such a gathering.

If they give the money as a gift to you, without you asking for it then you can keep it.

QUESTION: If my family insists me on celebrating my birthday even if i refuse to it but they will still buy cake and will celebrate so can i just ask my mom to give me the money instead so i can buy something else from that without celebrating it