What is the sum of the three digit cubes that are the cubes of either squares or cubes?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
What is the sum of the three digit cubes that are the cubes of either squares or cubes?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
1241
What is the sum of the three digit cubes that are the cubes of either squares or cubes?
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