Factoring (a + b)³  8b³
This expression can be factored using the difference of cubes formula.
The difference of cubes formula is:
a³  b³ = (a  b)(a² + ab + b²)
Let's apply this to our expression:

Recognize the cubes:
 (a + b)³ is the cube of (a + b)
 8b³ is the cube of 2b

Substitute into the formula:
 Let a = (a + b)
 Let b = 2b
Now we can rewrite the expression:
(a + b)³  8b³ = [(a + b)  2b][(a + b)² + (a + b)(2b) + (2b)²]

Simplify:
 [(a + b)  2b] = a  b
 [(a + b)² + (a + b)(2b) + (2b)²] = a² + 2ab + b² + 2ab + 2b² + 4b² = a² + 4ab + 7b²

Final factored expression:
(a + b)³  8b³ = (a  b)(a² + 4ab + 7b²)
Therefore, the factored form of (a + b)³  8b³ is (a  b)(a² + 4ab + 7b²).