The given expression is \( 8b^3 + 27 \), which can be factored as a sum of cubes.

### Sum of cubes formula:
\[
a^3 + b^3 = (a + b)(a^2 - ab + b^2)
\]

Here, we can rewrite \( 8b^3 + 27 \) as:
\[
(2b)^3 + 3^3
\]

Now apply the sum of cubes formula:
\[
(2b + 3)\left((2b)^2 - (2b)(3) + 3^2\right)
\]

Simplify the second factor:
\[
(2b + 3)(4b^2 - 6b + 9)
\]

So, the factored form of \( 8b^3 + 27 \) is:
\[
(2b + 3)(4b^2 - 6b + 9)
\]

Would you like more details or have any other questions?

Here are five related questions you might find useful:
1. How would you factor a difference of cubes, like \( a^3 - b^3 \)?
2. What are some common methods for factoring polynomials?
3. How can you identify if an expression is a perfect cube?
4. Can you factor a cubic polynomial with non-perfect cube terms?
5. How does factoring help solve polynomial equations?

**Tip**: When factoring, always look for common patterns like the sum or difference of cubes, perfect squares, or common factors!

Learn how to factor the cubic expression 8b^3 + 27 using the sum of cubes formula. This detailed step-by-step solution demonstrates the application of the sum of cubes theorem, perfect for students in Grades 9-11 looking to master factoring cubic polynomials.

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