To solve the given expressions, we need to expand or simplify them as required. Let's go through each one:

1) \((2x + 1)^3\)

Using the binomial theorem:
\[
(2x + 1)^3 = (2x)^3 + 3(2x)^2(1) + 3(2x)(1)^2 + (1)^3
\]
\[
= 8x^3 + 12x^2 + 6x + 1
\]

2) \((3 - 2b)^3\)

Using the binomial theorem:
\[
(3 - 2b)^3 = (3)^3 + 3(3)^2(-2b) + 3(3)(-2b)^2 + (-2b)^3
\]
\[
= 27 - 54b + 36b^2 - 8b^3
\]

3) \(8 - 27x^3\)

This expression is already simplified. It cannot be factored further without additional context or constraints.

4) \(64x^3 + 125y^3\)

This is a sum of cubes, which can be factored using the sum of cubes formula \(a^3 + b^3 = (a + b)(a^2 - ab + b^2)\):
\[
64x^3 + 125y^3 = (4x)^3 + (5y)^3
\]
\[
= (4x + 5y)((4x)^2 - (4x)(5y) + (5y)^2)
\]
\[
= (4x + 5y)(16x^2 - 20xy + 25y^2)
\]

So the solutions are:
1) \(8x^3 + 12x^2 + 6x + 1\)
2) \(27 - 54b + 36b^2 - 8b^3\)
3) \(8 - 27x^3\)
4) \((4x + 5y)(16x^2 - 20xy + 25y^2)\)