To factor the expression $x^3 - y^3$, we use the difference of cubes formula:

$a^3 - b^3 = (a - b)(a^2 + ab + b^2)$

Here, $a = x$ and $b = y$. Applying the formula, we get:

$x^3 - y^3 = (x - y)(x^2 + xy + y^2)$

So, the factored form of $x^3 - y^3$ is:

$x^3 - y^3 = (x - y)(x^2 + xy + y^2)$

Would you like further details or have any questions about this factorization?

Here are some related questions to explore this topic further:

1. How would you factor $x^3 + y^3$?
2. What is the factored form of $a^3 - b^3$ if $a = 2$ and $b = 3$?
3. How can you apply the difference of cubes formula to solve $27x^3 - 8y^3$?
4. What is the expanded form of $(x - y)(x^2 + xy + y^2)$?
5. Can you factor $x^3 - 1$ using the difference of cubes formula?

Tip: Remember that the difference of cubes formula can be very useful in simplifying expressions and solving equations that involve cubic terms.