which of the following are cubes of :
an odd number 216, 729, 3375 , 8000, 125 , 343, 4096 and 9261.

Answer

To determine which of the given numbers are cubes of odd numbers, we will analyze each number step by step.

### Step 1: Understand the properties of cubes
The cube of an odd number is always odd. This means that if a number is even, it cannot be the cube of an odd number.

### Step 2: List the given numbers
The numbers we need to analyze are:
- 216
- 729
- 3375
- 8000
- 125
- 343
- 4096
- 9261

### Step 3: Identify even and odd numbers
Now, we will identify which of these numbers are odd:
- **216**: Even
- **729**: Odd
- **3375**: Odd
- **8000**: Even
- **125**: Odd
- **343**: Odd
- **4096**: Even
- **9261**: Odd

### Step 4: Analyze the odd numbers
Next, we will check if the odd numbers (729, 3375, 125, 343, and 9261) are cubes of odd numbers.

1. **729**:
- \( 9^3 = 729 \) (9 is odd)

2. **3375**:
- \( 15^3 = 3375 \) (15 is odd)

3. **125**:
- \( 5^3 = 125 \) (5 is odd)

4. **343**:
- \( 7^3 = 343 \) (7 is odd)

5. **9261**:
- \( 21^3 = 9261 \) (21 is odd)

### Step 5: Conclusion
The numbers that are cubes of odd numbers are:
- 729
- 3375
- 125
- 343
- 9261

### Final Answer:
The cubes of odd numbers from the given list are: **729, 3375, 125, 343, and 9261.**

---