To solve this problem, we can observe that the numbers in the right-most column are cubes:

• $512 = 8^3$
• $1728 = 12^3$
• $2197 = 13^3$

It seems that the numbers in the right column follow the cube pattern.

Now, let's analyze the middle column to see if a similar pattern emerges:

• $10$, $25$, and the missing number are part of this column.
• These numbers could correspond to squares:
  • $10$ doesn't follow the square pattern, but $25 = 5^2$.
  • The missing number likely needs to fit into a pattern related to these numbers. Notice that 25 is the square of 5, and possibly the next number is also a square.

Next, the left column appears to have no cube or square pattern, so it might involve a different type of sequence, such as adding numbers.

Given this, we hypothesize that the missing number could logically be $6^2 = 36$, which fits between 5 and the higher values seen in the grid.

Thus, the missing number is 36, and the correct answer is C.

Would you like more details on this reasoning or any related questions? Here are 5 questions to expand your understanding:

1. How do cube numbers grow, and why are they used in sequences?
2. Could other patterns, like differences between numbers, be used to solve such problems?
3. Why do square and cube patterns appear so frequently in math puzzles?
4. Can this technique be applied to larger grids or matrices with more rows and columns?
5. How do these sequences relate to number theory or algebraic properties?

Tip: When working with sequences in grids, always check for powers, like squares or cubes, as they often form the basis of the pattern!