125

Number
$125$ (one hundred and twenty-five) is:


 * $5^3$


 * The $5$th cube number after $1, 8, 27, 64$:
 * $125 = 5 \times 5 \times 5$


 * The $13$th trimorphic number after $1, 4, 5, 6, 9, 24, 25, 49, 51, 75, 76, 99$:
 * $125^3 = 1 \, 953 \, \mathbf {125}$


 * The $17$th powerful number after $1, 4, 8, 9, 16, 25, 27, 32, 36, 49, 64, 72, 81, 100, 108, 121$


 * The length of the shortest face diagonal of the smallest cuboid whose edges and the diagonals of whose faces are all integers:
 * The lengths of the edges are $44, 117, 240$
 * The lengths of the diagonals of the faces are $125, 244, 267$.


 * The $10$th integer after $7, 13, 19, 35, 38, 41, 57, 65, 70$ the decimal representation of whose square can be split into two parts which are each themselves square:
 * $125^2 = 15 \, 625; 1 = 1^2, 5625 = 75^2$


 * The $4$th positive integer after $50, 65, 85$, and first cube, which can be expressed as the sum of two square numbers in two or more different ways:
 * $125 = 11^2 + 2^2 = 10^2 + 5^2 = 5^3$

Also see

 * Cuboid with Integer Edges and Face Diagonals