To solve the given expressions using the formulas for binomial expansion, we can apply the expansions for \((A + B)^3\) and \((A - B)^3\).

### Binomial Expansion:
1. **Expansion Formulae:**
- \((A + B)^3 = A^3 + 3A^2B + 3AB^2 + B^3\)
- \((A - B)^3 = A^3 - 3A^2B + 3AB^2 - B^3\)

### Task 1: Expand \((A + B)^3\)
- **Examples:**
1. \((a + 2)^3\)
\[
A = a, \quad B = 2
\]
\[
= a^3 + 3a^2(2) + 3a(2)^2 + 2^3 = a^3 + 6a^2 + 12a + 8
\]

2. \((2 + 3x)^3\)
\[
A = 2, \quad B = 3x
\]
\[
= 2^3 + 3 \cdot 2^2 (3x) + 3 \cdot 2(3x)^2 + (3x)^3 = 8 + 36x + 54x^2 + 27x^3
\]

### Task 2: Expand \((A - B)^3\)
- **Examples:**
1. \((a - 2)^3\)
\[
A = a, \quad B = 2
\]
\[
= a^3 - 3a^2(2) + 3a(2)^2 - 2^3 = a^3 - 6a^2 + 12a - 8
\]

2. \((x - 5)^3\)
\[
A = x, \quad B = 5
\]
\[
= x^3 - 3x^2(5) + 3x(5)^2 - 5^3 = x^3 - 15x^2 + 75x - 125
\]

### Task 3: Cube Sums and Differences
- **Sum and Difference of Cubes:**
- \(A^3 + B^3 = (A + B)(A^2 - AB + B^2)\)
- \(A^3 - B^3 = (A - B)(A^2 + AB + B^2)\)

### Examples:
- Given \((3b)^2 = 25a^2 - 9b^2\), you might want to relate this to cube identities for tasks that involve sum and difference of cubes.

Using these expansions and identities, you should be able to approach and solve each of your given problems as needed. If you have any specific question on the order of solving or a particular expression you want further help with, feel free to ask!