1. The problem is to expand the expression $ (1 + b)^3 $. 2. We use the binomial expansion formula for cubes: $$ (a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3 $$ where $a = 1$ and $b = b$. 3. Substitute $a = 1$ into the formula: $$ (1 + b)^3 = 1^3 + 3 \times 1^2 \times b + 3 \times 1 \times b^2 + b^3 $$ 4. Simplify each term: $$ = 1 + 3b + 3b^2 + b^3 $$ 5. This is the fully expanded form of $ (1 + b)^3 $. Final answer: $$ (1 + b)^3 = 1 + 3b + 3b^2 + b^3 $$