The cubes on the surface are all painted with color, except for the outer layer, that is, the length, width and height are reduced by a long distance from both sides, and the inside is a small cube without color.

Total number of small cubes = 7 * 9 *11+5 * 7 * 9+9 * 3 * 7 =1197 (pieces)

No red total = (7-2) (9-2) (11-2)+(5-2) (7-2) (9-2)+(9-2) (3-2) (7-2) = 445.

Therefore, there are 1 197-445=752 small cubes with at least one side red.

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