The expression \( a^3 + 64 \) can be factored using the sum of cubes formula. The sum of cubes formula is given by:

\[
x^3 + y^3 = (x + y)(x^2 - xy + y^2)
\]

In this case, \( a^3 + 64 \) can be rewritten as:

\[
a^3 + 4^3
\]

Now, apply the sum of cubes formula:

\[
a^3 + 4^3 = (a + 4)(a^2 - 4a + 16)
\]

So, the factored form of \( a^3 + 64 \) is:

\[
(a + 4)(a^2 - 4a + 16)
\]

Would you like more details or have any other questions? 

Here are 5 related questions:

1. How do you factor a difference of cubes?
2. What is the general form of the sum of cubes?
3. How can the quadratic formula be applied to the quadratic term in this factorization?
4. What are the roots of the quadratic \( a^2 - 4a + 16 \)?
5. How can the factorization of cubes be applied in solving polynomial equations?

**Tip:** Always remember that cubes can be factored using specific formulas for both the sum and difference of cubes.

Learn how to factor the expression a^3 + 64 using the sum of cubes formula with a detailed step-by-step solution. This problem covers algebraic concepts including the sum of cubes formula. Suitable for advanced high school students.

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