Find the odd one out.
729, 1331, 2197, 3125

To find the odd one out from the given set of numbers (729, 1331, 2197, 3125), let us analyze the mathematical pattern behind each number.

Let us express each number in terms of its powers or prime factorizations:

${729}^{}$ is equal to $9^3$ (a perfect cube of 9).

${1331}^{}$ is equal to ${11}^3$ (a perfect cube of 11).

${2197}^{}$ is equal to ${13}^3$ (a perfect cube of 13).

${3125}^{}$ is equal to $5^5$ (or ${25}^2\times 5$), which is a fifth power, not a perfect cube of an integer (since the cube root of 3125 is approximately 14.62).

As we can see, 729, 1331, and 2197 are all perfect cubes, whereas 3125 is not a perfect cube.
Therefore, 3125 is the odd one out.

The correct option is 3125.