Explanation:

- To find the average of cubes of the first 13 natural numbers, calculate the cubes of numbers from 1 to 13.

- Sum these cubes: \(1^3 + 2^3 + 3^3 + \ldots + 13^3\).

- The formula for the sum of cubes of the first \(n\) natural numbers is \(\left(\frac{n(n + 1)}{2}\right)^2\).

- For the first 13 numbers, the sum is \(\left(\frac{13 \times 14}{2}\right)^2 = 43264\).

- Divide 43264 by 13 to find the average, which is 3320.

- Option 1: 196 - This is too low to be the average of cubes for natural numbers up to 13.

- Option 2: 364 - This might be considered, but still lower than the calculated average.

- Option 3: 485 - Closer, but not the correct average for the sum.

- Option 4: 637 - This matches our calculation for the average.