The cube of an even number is always an even number. Let's understand why this is the case.

Explanation:

1. Understanding Even Numbers:
- Even numbers are those numbers that are divisible by 2 without leaving a remainder.
- Examples of even numbers include 2, 4, 6, 8, 10, and so on.

2. Cubing an Even Number:
- When we cube a number, we multiply it by itself twice.
- For example, the cube of 2 is calculated as 2 * 2 * 2 = 8.
- Similarly, the cube of 4 is calculated as 4 * 4 * 4 = 64.

3. Multiplying Even Numbers:
- When we multiply even numbers together, the product is always an even number.
- This can be understood by considering the definition of even numbers.
- Since even numbers are divisible by 2, when we multiply two even numbers, each of them can be expressed as 2 multiplied by some other number.
- Therefore, the product of two even numbers can be written as (2 * a) * (2 * b), where 'a' and 'b' are some other numbers.
- Simplifying this expression, we get 4 * (a * b), which is again divisible by 2 without leaving a remainder.
- Hence, the product of two even numbers is always an even number.

4. Cubing Even Numbers:
- When we cube an even number, we are essentially multiplying it by itself twice.
- Since multiplying two even numbers always results in an even number, it follows that the cube of an even number will also be an even number.

Conclusion:
- The cube of an even number is always an even number because even numbers are divisible by 2, and multiplying even numbers always results in an even number.