Let's solve the given expression step by step:

The equation is:

$3^3 + 4(8 - 5) \div 6 = ?$

Step 1: Simplify the powers

$3^3 = 3 \times 3 \times 3 = 27$

Step 2: Simplify inside the parentheses

$8 - 5 = 3$

The equation becomes: $27 + 4(3) \div 6$

Step 3: Multiply and divide from left to right (following the order of operations, PEMDAS/BODMAS):

First, calculate $4 \times 3$: $4 \times 3 = 12$

Next, divide: $12 \div 6 = 2$

Now the equation becomes: $27 + 2$

Step 4: Add

$27 + 2 = 29$

Final Answer:

$\boxed{29}$

Let me know if you'd like a detailed explanation or clarification on any part of this!

Related Questions:

1. What are the steps of PEMDAS/BODMAS, and why is the order important?
2. How do you simplify powers and exponents?
3. What happens if parentheses are omitted in expressions like this?
4. Can you show examples where division happens before multiplication in similar problems?
5. How can parentheses change the final result of an equation?

Tip:

Always tackle problems like this systematically, following PEMDAS/BODMAS to avoid errors in the order of operations!