The given expression is $x^3 + 27y^3$. This expression can be factored using the sum of cubes formula. The sum of cubes formula is given by:

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

In this case, $a = x$ and $b = 3y$. Applying the formula, we get:

$x^3 + 27y^3 = (x + 3y)(x^2 - x \cdot 3y + (3y)^2)$

Simplifying inside the parentheses:

$x^3 + 27y^3 = (x + 3y)(x^2 - 3xy + 9y^2)$

So, the factored form of $x^3 + 27y^3$ is:

$x^3 + 27y^3 = (x + 3y)(x^2 - 3xy + 9y^2)$

Would you like more details or have any questions?

Here are 5 numbered questions you might ask:

1. How do you factor the difference of cubes?
2. Can you provide an example using a different sum of cubes?
3. What is the sum of cubes formula used for?
4. How can you verify that the factorization is correct?
5. Can you explain the difference between the sum of cubes and the difference of cubes formulas?

Tip: When factoring polynomials, always look for common patterns like the sum or difference of cubes, which can simplify the problem significantly.