The given expression is $x^3 + 125$. This is a sum of cubes, since $125 = 5^3$. The sum of cubes can be factored using the following identity:

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

In this case, $a = x$ and $b = 5$, so we can rewrite the expression as:

$x^3 + 125 = (x + 5)(x^2 - 5x + 25)$

Thus, the factored form of $x^3 + 125$ is:

$(x + 5)(x^2 - 5x + 25)$

Would you like any further explanation or details?

Here are 5 related questions for deeper understanding:

1. How can we factor the difference of cubes?
2. What are some real-life applications of factoring cubic expressions?
3. Can the quadratic factor $x^2 - 5x + 25$ be factored further?
4. How do you find the roots of a cubic equation?
5. What is the graphical representation of $x^3 + 125$?

Tip: For cubic equations, always check if the sum or difference of cubes formula applies to simplify them easily.