Answer: There are 2 acceptable answers, the one that is provided in the book that this was taken from, and another answer which I feel is also correct:

Book's answer: He multiples the cube number 8 by 27, then removes 1 (1 cubed) from the resultant number 216 to leave 26.

My answer: Add 1 cubed 27 times to get 27, which is 3 cubed. In the original equation (1 cubed, added together 27 times), remove the center 1 cubed, the resulting sum being 26.

Source: This puzzle was used (with permission) from Lloyd King's' book Test Your Creative Thinking: Enhance Your Lateral Thinking - Learn to Think Outside the Box.

Winner: Tim, Cleveland, OH