### 4 integers between 100 and 999, inclusive, which equal the sum of the cubes of their digits

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?

SMALL HINT

BIGGER HINT

SOLUTION

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