1. The problem is to simplify the expression $13 + 3^3 \times 2$ using the order of operations. 2. According to the order of operations (PEMDAS/BODMAS), we first evaluate exponents, then multiplication and division from left to right, and finally addition and subtraction. 3. Calculate the exponent: $3^3 = 27$. 4. Substitute back into the expression: $13 + 27 \times 2$. 5. Next, perform the multiplication: $27 \times 2 = 54$. 6. Substitute back: $13 + 54$. 7. Finally, perform the addition: $13 + 54 = 67$. 8. Therefore, the simplified expression is $67$.