To solve the expression $2^3 + 4 \times (5 - 2)$, we follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

1. Parentheses: First, solve the expression inside the parentheses: $5 - 2 = 3$

2. Exponents: Next, calculate the exponent: $2^3 = 8$

3. Multiplication: Then, perform the multiplication: $4 \times 3 = 12$

4. Addition: Finally, add the results: $8 + 12 = 20$

Therefore, the value of the expression $2^3 + 4 \times (5 - 2)$ is $20$.

Would you like more details or have any questions?

Here are some related questions to consider:

1. How would the result change if we had $2^3 + 4 \times (5 - 3)$?
2. What if the exponent was applied to the entire $4 \times (5-2)$ term?
3. How does the order of operations affect expressions without parentheses?
4. Can the order of operations lead to different results if done incorrectly?
5. How would you solve an expression with both fractions and exponents?

Tip: Always handle parentheses first in any mathematical expression to simplify the rest of the calculations!