125

125 is a perfect cube, 5³.

125 is the smallest cube that is also the sum of two squares in two different ways: 125 = 11² + 2² = 10² + 5².

5³ – 2⁷ = 5 – 2. The only known matching pattern is 13³ – 3⁷ = 13 – 3.

125 is the hypotenuse of a primitive Pythagorean triple: 125² = 44² + 117².

Space Shuttle mission STS-125 was the final servicing mission to the Hubble Space Telescope.

Source: The Penguin Dictionary of Curious and Interesting Numbers, rev. ed., by David Wells.