What is the smallest two-digit prime that is the sum of three (not necessarily distinct) positive perfect cubes?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
What is the smallest two-digit prime that is the sum of three (not necessarily distinct) positive perfect cubes?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
17
What is the smallest two-digit prime that is the sum of three (not necessarily distinct) positive perfect cubes?
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