How many triples $(a,b,c)$ of even positive integers satisfy $a^3 + b^2 + c \leq 50$?
<|im_start|>system
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<|im_start|>user
How many triples $(a,b,c)$ of even positive integers satisfy $a^3 + b^2 + c \leq 50$?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
35
How many triples $(a,b,c)$ of even positive integers satisfy $a^3 + b^2 + c \leq 50$?
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