Evaluate: `(2a + 3b)^(3)`

Answer

To evaluate \((2a + 3b)^{3}\), we will use the formula for the cube of a binomial, which states that:

\[ (a + b)^{3} = a^{3} + b^{3} + 3a^{2}b + 3ab^{2} \]

### Step-by-Step Solution:

1. **Identify \(a\) and \(b\)**:
- Here, let \(a = 2a\) and \(b = 3b\).

2. **Calculate \(a^{3}\)**:
- \(a^{3} = (2a)^{3} = 2^{3} \cdot a^{3} = 8a^{3}\).

3. **Calculate \(b^{3}\)**:
- \(b^{3} = (3b)^{3} = 3^{3} \cdot b^{3} = 27b^{3}\).

4. **Calculate \(3a^{2}b\)**:
- \(3a^{2}b = 3 \cdot (2a)^{2} \cdot (3b) = 3 \cdot 4a^{2} \cdot 3b = 36a^{2}b\).

5. **Calculate \(3ab^{2}\)**:
- \(3ab^{2} = 3 \cdot (2a) \cdot (3b)^{2} = 3 \cdot 2a \cdot 9b^{2} = 54ab^{2}\).

6. **Combine all parts**:
- Now, we combine all these results:
\[ (2a + 3b)^{3} = a^{3} + b^{3} + 3a^{2}b + 3ab^{2} \]
\[ = 8a^{3} + 27b^{3} + 36a^{2}b + 54ab^{2} \]

### Final Answer:
\[ (2a + 3b)^{3} = 8a^{3} + 27b^{3} + 36a^{2}b + 54ab^{2} \]