On a $3\times3\times3$ cube, all but one $1\times1\times1$ are visible.

How many $1\times1\times1$ cubes are visible on the surface of a $10\times10\times10$ cube?

The answer is 488.

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The answer is $10^3 - 8^3 = 1000 - 512 = \boxed{488}$