Let's break down the given expression step by step to understand it.

### Step 1: Simplify the expression \((2+3)(2^2-6+9^2)\)

1. First, simplify each component:
   - \( 2 + 3 = 5 \)
   - \( 2^2 = 4 \)
   - \( 9^2 = 81 \)
   - So, \( 2^2 - 6 + 9^2 = 4 - 6 + 81 = -2 + 81 = 79 \)

2. Now, multiply the simplified parts:
   \[
   (2+3)(2^2-6+9^2) = 5 \times 79 = 395
   \]

### Step 2: Sum of Two Cubes

The sum of two cubes is expressed as:

\[
a^3 + b^3 = (a + b)(a^2 - ab + b^2)
\]

However, in the expression you provided, there isn't an apparent "sum of two cubes" situation. If you intended to find a sum of cubes or factor an expression like \(a^3 + b^3\), please clarify the specific expression you'd like to factor or analyze.

Would you like more details or have any questions?

Here are 5 related questions you might consider:
1. What is the difference between the sum of cubes and the difference of cubes?
2. How do you factor \(8x^3 + 27\) as a sum of cubes?
3. Can you apply the sum of cubes to negative numbers?
4. What are the real-life applications of factoring the sum of cubes?
5. How would you solve an equation involving the sum of cubes, such as \(x^3 + 27 = 0\)?

**Tip:** When dealing with algebraic expressions, carefully simplify each part before combining them to avoid mistakes in calculations.

Learn how to simplify algebraic expressions and apply the sum of cubes formula. This problem involves breaking down complex expressions and understanding algebraic identities. Suitable for students in Grades 9-12.

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