Calculate the cube of any number with step-by-step solutions, perfect cube detection, and geometry connections.
Cube
125
Enter any number (positive, negative, or decimal)
53 = 125
Real-world cube measurements
Given number: 5
Formula: n^3 = n x n x n
Calculation: 5^3 = 5 x 5 x 5
Step 1: 5 x 5 = 25
Step 2: 25 x 5 = 125
Result: 125
A cube with side length 5 units has a volume of 125 cubic units. This is because Volume = side x side x side = 5 x 5 x 5 = 125.
Volume = 5^3 = 125 cubic units
Cube
125
To cube a number, multiply it by itself three times: n^3 = n x n x n. For example, 4^3 = 4 x 4 x 4 = 64. Unlike squaring, cubing preserves the sign: (-2)^3 = -8 (negative), while (2)^3 = 8 (positive). Perfect cubes are integers resulting from cubing integers: 1, 8, 27, 64, 125, 216...
Cubing a number means raising it to the third power, or multiplying it by itself three times. The cube of n, written as n^3 or n cubed, equals n x n x n. Geometrically, the cube of a number represents the volume of a cube whose sides have that length. Cubing appears in physics (volume calculations), chemistry (molar relationships), and advanced mathematics.
Test your understanding of cubes
Practice with 4 problems to test your understanding.
Cubing a number means multiplying it by itself three times. For example, 4 cubed (4^3) equals 4 x 4 x 4 = 64. The result represents the volume of a cube with that side length.
The cube of a negative number is always negative. This is because negative x negative x negative = negative. For example, (-3)^3 = (-3) x (-3) x (-3) = 9 x (-3) = -27.
A perfect cube is an integer that results from cubing another integer. Examples include 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, etc. These are the cubes of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, respectively.
The cube of a number n represents the volume of a cube with side length n. For example, a cube with sides of 3 units has a volume of 3^3 = 27 cubic units. This is why we call it "cubing" a number.
Cubes grow much faster than squares. For example: 10^2 = 100 but 10^3 = 1000. At n=100: 100^2 = 10,000 but 100^3 = 1,000,000. The difference becomes more dramatic as n increases.
Last updated: 2025-01-15
Cube
125