1. The problem is to find the value of the expression $e^3$. 2. Here, $e$ is the mathematical constant approximately equal to 2.71828. 3. The expression $e^3$ means $e$ raised to the power 3, which is calculated as $e \times e \times e$. 4. Using a calculator or software, $e^3 \approx 2.71828^3 \approx 20.0855$. 5. Therefore, the value of $e^3$ is approximately $20.0855$.