Question: Evaluate the following expression.
$8^3 - 9\cdot 2 \div 3 =$
1. **State the problem:** Evaluate the expression $$8^3 - 9 \cdot 2 \div 3$$.
2. **Recall order of operations:** Use PEMDAS (Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction).
3. **Calculate the exponent:** $$8^3 = 8 \times 8 \times 8 = 512$$.
4. **Perform multiplication and division from left to right:**
$$9 \cdot 2 \div 3 = \cancel{9 \cdot 2} \div 3 = 18 \div 3 = 6$$
5. **Substitute back into the expression:**
$$512 - 6$$
6. **Perform the subtraction:**
$$512 - 6 = 506$$
**Final answer:** $$506$$