There are several entries (examples) of "special products and factors."
x^2-y^2 = (x-y)(x+y)
x^3+y^3 = (x+y)(x^2-xy + y^2)
x^3 - y^3 = (x - y)(x^2 + xy + y^2)
The given expression, 27x^3 - 1, matches the format of the third example given above.
Note that 1 can be rewritten as 1^3 without changing its value.
Thus, The given expression, 27x^3 - 1, is the same as 27x^3 - 1^3, which in turn can be rewritten in the form x^3 - y^3:
27x^3 - 1^3 = (3x)^3 - 1^3. And so, the factors are (3x - 1)(9x^2 + 3x + 1)
It'd definitely be worth learning and memorizing the special products and factors listed above, as well as others.