Find the minimum value of $x^6 + y^6 - 54xy$ over all real numbers $x$ and $y.$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Find the minimum value of $x^6 + y^6 - 54xy$ over all real numbers $x$ and $y.$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
-108
Find the minimum value of $x^6 + y^6 - 54xy$ over all real numbers $x$ and $y.$
train