Step-by-step Solution:

Solution

The puzzle uses two different patterns: one for the numbers around the edge and a separate one for the center number.

Analysis of the Pattern:

• Outer Numbers: The numbers on the outside of the grid follow the pattern n² + 1. For example, 2 = 1² + 1, 5 = 2² + 1, 10 = 3² + 1, and so on, up to 82 = 9² + 1.
  
• Center Number: The missing number in the center follows a different rule based on the dimensions of the grid. The rule is m³, where 'm' is the number of rows/columns.
  

Conclusion:

Since the grid is 3x3, we use m = 3. The missing character is calculated as:
3³ = 27.