1. **State the problem:** Simplify or expand the expression $ (2x-1)^3 $. 2. **Formula used:** The cube of a binomial $(a-b)^3 = a^3 - 3a^2b + 3ab^2 - b^3$. 3. **Identify terms:** Here, $a = 2x$ and $b = 1$. 4. **Apply the formula:** $$ (2x-1)^3 = (2x)^3 - 3(2x)^2(1) + 3(2x)(1)^2 - 1^3 $$ 5. **Calculate each term:** $$ (2x)^3 = 8x^3 $$ $$ 3(2x)^2(1) = 3 \times 4x^2 \times 1 = 12x^2 $$ $$ 3(2x)(1)^2 = 6x $$ $$ 1^3 = 1 $$ 6. **Substitute back:** $$ (2x-1)^3 = 8x^3 - 12x^2 + 6x - 1 $$ 7. **Final answer:** $$ \boxed{8x^3 - 12x^2 + 6x - 1} $$