In the questions, there is a certain relationship between the two given numbers on one side of :: and one number is given on another side of :: . It is required to find another number from the given alternative having the same relationship with this number as the numbers of the given pair has :
2:9:: 6:?

Options

A. 27
B. 65
C. 217
D. 210

Explanation

To solve the analogy problem \( 2:9:: 6:? \), we need to identify the relationship between the numbers on the left side of the analogy and apply the same relationship to the number on the right side.

### Step-by-Step Solution:

1. **Identify the relationship between 2 and 9:**
- We need to find a mathematical operation that connects 2 to 9.
- By examining the numbers, we can see that \( 2^3 + 1 = 8 + 1 = 9 \).

2. **Apply the same relationship to the number 6:**
- Now, we will use the same operation on the number 6.
- Calculate \( 6^3 + 1 \):
- First, find \( 6^3 \):
\[ 6^3 = 6 \times 6 \times 6 = 216 \]
- Then, add 1:
\[ 216 + 1 = 217 \]

3. **Conclusion:**
- Therefore, the number that corresponds to 6 in the analogy \( 2:9:: 6:? \) is \( 217 \).

### Final Answer:
The answer is \( 217 \).