The function $f(x) = x^3$ is a polynomial function, and polynomial functions are continuous everywhere. Since $f(x)$ is continuous at $x = -3$, we can evaluate the limit by direct substitution.

So, we have:

$\lim_{{x \to -3}} f(x) = f(-3)$

Substitute $x = -3$ into the function:

$f(-3) = (-3)^3 = -27$

Therefore, the value of the limit is:

$\lim_{{x \to -3}} f(x) = -27$

Would you like more details or have any questions?

Here are 5 related questions to consider:

1. What does it mean for a function to be continuous at a point?
2. How would the solution change if $f(x) = x^2$ instead of $x^3$?
3. What is the general form of the derivative of $f(x) = x^n$?
4. How does the concept of limits relate to the derivative of a function?
5. Can a function be discontinuous but still have a limit at a particular point?

Tip: When evaluating limits of continuous functions, you can often directly substitute the value the variable is approaching into the function.