There are four integers between 100 and 999, inclusive, which equal the sums of the cubes of their digits. Three of them are 153, 370, and 407. For example, 153 = 1³ + 5³ + 3³. What is the fourth such integer?
Close examination of what each digit adds to its side of the equation for each of the three known solutions should lead you to the fourth 3-digit integer.