Sums and Differences of Cubes (and other odd powers)?

You can factor a sum or difference of cubes using the formulas
a³ - b ³ = (a - b )(a² + ab + b²)
and
a³ + b³ = (a + b)(a² - ab + b²).
For example,
y³ + 8
= y³ + 23
= (y + 2)(y² -2y + 4).
Here's another example:
x⁶ - 27
=(x² ) 3 - 33
=(x² -3 ) ((x²) 2 +3x² + 9)

= (x² -3 )(x⁴ + 3x² + 9).

How do you know if a monomial is a perfect cube? It's easy. It's a cube if

1. The coefficient is a perfect cube (it can be positive or negative);

2. All the exponents on the variables are multiples of 3.