Factorize completely 3x3 - 27

The given expression is $3x^3 - 27$.
The terms are $3x^3$ and $-27$.
The GCF of 3 and 27 is 3.
Factor out 3 from both terms:

$$3x^3 - 27 = 3(x^3 - 9)$$

The remaining polynomial is $x^3 - 9$.
This is not a difference of squares ($a^2 - b^2$) because the first term is cubed, not squared.
This is not a difference of cubes ($a^3 - b^3$) with integer bases, because 9 is not a perfect cube of an integer ($2^3 = 8$ and $3^3 = 27$).
Therefore, $x^3 - 9$ cannot be factored further into polynomials with integer coefficients.

The expression is completely factored as:

$$3(x^3 - 9)$$