To factor the expression $64 - w^3$, we recognize it as a difference of cubes since $64$ is a perfect cube ($64 = 4^3$) and $w^3$ is obviously a cube.

The difference of cubes formula is:

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

Here, $a = 4$ and $b = w$. So, applying the formula:

$64 - w^3 = (4 - w)(16 + 4w + w^2)$

Thus, the factored form of $64 - w^3$ is:

$(4 - w)(16 + 4w + w^2)$

Would you like details on the difference of cubes formula or have any questions?

Here are 5 related questions you might find interesting:

1. How do you factor the sum of cubes?
2. What is the general formula for factoring a cubic polynomial?
3. How can the difference of squares formula be derived?
4. What are other examples of expressions involving perfect cubes?
5. How do you expand the product of two binomials?

Tip: Always check if an expression fits known patterns like the difference of squares or cubes before attempting more complex factoring methods.