Factorize : `27 a^3+1/(64 b^3)+(27a^2)/(4b)+(9a)/(16 b^2)` `

Explanation

To factorize the expression \( 27 a^3 + \frac{1}{64 b^3} + \frac{27a^2}{4b} + \frac{9a}{16 b^2} \), we can follow these steps:

### Step 1: Identify the Cubes
We notice that \( 27 a^3 \) can be expressed as \( (3a)^3 \) and \( \frac{1}{64 b^3} \) can be expressed as \( \left(\frac{1}{4b}\right)^3 \).

### Step 2: Rewrite the Expression
We rewrite the expression using these cubes:
\[
...