To compute the cube of the number 3, we follow the process of cubing, which involves multiplying the number by itself twice. Hence, we perform $3 \times 3 \times 3$, which equals 27.

Elaborating further, cubing a number means raising it to the power of three. This process entails multiplying the number by itself two times. Considering the number 3 as an example, we begin by multiplying $3 \times 3$, yielding 9. This result is then multiplied again by 3, so $9 \times 3$ equals 27. Consequently, the cube of 3 is 27.

This process can be succinctly represented as $3^3$ in mathematical notation. The superscript 3 indicates that the number 3 is to be multiplied by itself three times. This is distinct from the process of squaring a number, which entails only a single self-multiplication (e.g., $3^2 = 3 \times 3 = 9$).

The ability to cube a number is a valuable skill in multiple fields of mathematics, including geometry and algebra. For instance, in computing the volume of a cube, the formula $V = s^3$ is used, where $s$ represents the length of one side of the cube. Consequently, if the length of each side of the cube is 3 units, the volume would be $3^3 = 27$ cubic units.

Keep in mind that the process of cubing a number is quite straightforward: simply multiply the number by itself two times. Regular practice with various numbers can enhance your comprehension of this concept.