To solve the expression \(\frac{27x^3 + 27x^2 + 9x + 1}{(3x+1)^2}\), we can start by factoring the numerator.

First, let's rewrite the numerator in a more recognizable form:
\[ 27x^3 + 27x^2 + 9x + 1 \]

Notice that \(27x^3\) can be written as \((3x)^3\), \(27x^2\) can be written as \(3 \cdot (3x)^2\), \(9x\) can be written as \(3^2 \cdot x\), and \(1\) can be written as \(1^3\).

So, the numerator can be rewritten as:
\[ (3x+1)^3 \]

Now, the expression becomes:
\[ \frac{(3x+1)^3}{(3x+1)^2} \]

By simplifying, we get:
\[ (3x+1) \]

Thus, the correct answer is:
\[ \boxed{B. \ 3x+1} \]