When evaluating a limit like $\frac{x^3 - a^3}{x - a}$, use the difference of cubes identity:

Example:

1. Recognize $8 = 2^3$
2. Apply identity:

3. Cancel $x - 2$
4. Evaluate at $x = 2$: $4 + 4 + 4 = 12$

This method avoids undefined division and simplifies the expression cleanly.