In this case, "X:X is a perfect cube" suggests that $X$ is a number that is a perfect cube. A perfect cube is a number that can be expressed as $a^3$, where $a$ is an integer. This implies that $X = a^3$ for some integer $a$.

For example:

• $8$ is a perfect cube because $2^3 = 8$,
• $27$ is a perfect cube because $3^3 = 27$,
• $64$ is a perfect cube because $4^3 = 64$, and so on.

Do you want more details on perfect cubes or examples of how to find them?

Here are some questions to deepen understanding:

1. What are the properties of perfect cubes?
2. How do you check if a given number is a perfect cube?
3. Can perfect cubes be negative numbers? Why?
4. How does the concept of a perfect cube extend to higher dimensions (e.g., algebra)?
5. Can non-integer numbers have perfect cubes?

Tip: The cube root of a perfect cube is always an integer. This makes it easy to identify perfect cubes!