Factor 27x^3 - 1

I know the answer, but I really need an explanation on factoring. I can't seem to get it down.

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.