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.