1. Problem: Compute $62^3$. 2. Formula: For any number $a$, $a^3 = a \times a \times a$. 3. Important rules: Exponentiation means repeated multiplication and $a^m \times a^n = a^{m+n}$. 4. Compute $62^2 = 62 \times 62 = 3844$. 5. Then $62^3 = 62^2 \times 62 = 3844 \times 62$. 6. Multiply using distribution: $3844 \times 62 = 3844 \times (60 + 2) = 3844 \times 60 + 3844 \times 2$. 7. Evaluate: $3844 \times 60 = 230640$. 8. Evaluate: $3844 \times 2 = 7688$. 9. Sum: $230640 + 7688 = 238328$. 10. Final answer: $62^3 = 238328$.