To solve the polynomial equation \(27x^3 - 54x^2 + 36x - 8 = 0\), we can start by looking for rational roots using the Rational Root Theorem, synthetic division, or factoring.

### Step 1: Check for Rational Roots
Using the Rational Root Theorem, we can test possible rational roots, which are the factors of the constant term (-8) divided by the factors of the leading coefficient (27).

The possible rational roots are \(\pm 1, \pm 2, \pm 4, \pm 8, \pm \frac{1}{3}, \pm \frac{2}{3}, \pm \frac{4}{3}, \pm \frac{8}{3}, \pm \frac{1}{27}, \pm \frac{2}{27}, \pm \frac{4}{27}, \pm \frac{8}{27}\).

### Step 2: Test Rational Roots
We can start by testing \(x = \frac{2}{3}\):
\[
27\left(\frac{2}{3}\right)^3 - 54\left(\frac{2}{3}\right)^2 + 36\left(\frac{2}{3}\right) - 8
\]

Calculating each term:
\[
= 27\left(\frac{8}{27}\right) - 54\left(\frac{4}{9}\right) + 36\left(\frac{2}{3}\right) - 8
\]
\[
= 8 - 24 + 24 - 8 = 0
\]

### Step 3: Factor the Polynomial
Since \(x = \frac{2}{3}\) is a root, we can use synthetic division or factorization.

Using synthetic division with the root \(\frac{2}{3}\):
```
(2/3 | 27 -54 36 -8
| 18 -24 8
---------------------------------
27 -36 12 0
```

The quotient is \(27x^2 - 36x + 12\).

### Step 4: Factor the Remaining Quadratic
Next, we can factor \(27x^2 - 36x + 12\):
\[
27x^2 - 36x + 12 = 0
\]

To factor, we can first simplify:
\[
3(9x^2 - 12x + 4) = 0
\]
Now factoring \(9x^2 - 12x + 4\):
\[
= (3x - 2)(3x - 2) = (3x - 2)^2
\]

### Step 5: Complete Factored Form
So, we have:
\[
(3x - 2)^2 = 0 \implies 3x - 2 = 0 \implies x = \frac{2}{3}
\]

### Conclusion
The polynomial \(27x^3 - 54x^2 + 36x - 8 = 0\) has a triple root at:
\[
\boxed{\frac{2}{3}}
\]