Let P (n) be the statement `2^(3n) - 1` is integral multiple of 7. Then P (3) is true.

Answer

To solve the problem, we need to verify the statement \( P(3) \) which asserts that \( 2^{3n} - 1 \) is an integral multiple of 7 for \( n = 3 \).

### Step-by-Step Solution:

1. **Substitute \( n = 3 \) into the expression**:
\[ P(3) : 2^{3 \cdot 3} - 1 = 2^9 - 1 \]

2. **Calculate \( 2^9 \)**:
\[ 2^9 = 512 \]

3. **Subtract 1 from \( 2^9 \)**:
\[ 2^9 - 1 = 512 - 1 = 511 \]

4. **Check if 511 is an integral multiple of 7**:
To determine if 511 is divisible by 7, we perform the division:
\[ 511 \div 7 = 73 \]
Since 73 is an integer, this means that 511 is indeed an integral multiple of 7.

5. **Conclusion**:
Since \( 511 \) is divisible by \( 7 \), we conclude that \( P(3) \) is true.

### Final Answer:
Thus, the statement \( P(3) \) is true.

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