To factor the given expression, we can first use grouping.

Grouping:

X^3 - 18x^2 + 108x - 216 = 0

Factor out common terms from the first two terms and the last two terms:

x^2(x - 18) + 108(x - 18) = 0

Now, factor out the common binomial factor (x - 18):

(x^2 + 108)(x - 18) = 0

Now we have a quadratic expression that can be factored further:

(x^2 + 108) = 0
x^2 = -108
x = ±√(-108)
Since -108 is negative, it does not have a real square root.

Therefore, the only real root of the equation x^3 - 18x^2 + 108x - 216 = 0 is x = 18.