A solid 6-by-6-by-6 cube is constructed from unit cubes and the entire outer surface is painted. What fraction of the unit cubes has at least two painted faces? Express your answer as a common fraction.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
A solid 6-by-6-by-6 cube is constructed from unit cubes and the entire outer surface is painted. What fraction of the unit cubes has at least two painted faces? Express your answer as a common fraction.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\frac{7}{27}
A solid 6-by-6-by-6 cube is constructed from unit cubes and the entire outer surface is painted. What fraction of the unit cubes has at least two painted faces? Express your answer as a common fraction.
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