s³ + s² - 8m³ - 4m²

Swap the middle two terms:

s³ - 8m³ + s² - 4m²

Rewrite as

(s³ - 8m³) + (s² - 4m²)

The first parenthese contains a difference of two cubes and
the second parentheses contains a difference of two squares.
You have studied how to factor these.

(s - 2m)(s² + 2sm + 4m²) + (s - 2m)(s + 2m)

Next we factor out the common factor (s - 2m) using brackets:

(s - 2m)[(s² + 2sm + 4m²) + (s + 2m)]

Remove the parentheses inside the brackets

(s - 2m)[s² + 2sm + 4m² + s + 2m]

Change the brackets to parentheses:

(s - 2m)(s² + 2sm + 4m² + s + 2m)

Edwin