Let's expand and compute the powers of each expression provided one by one using the binomial theorem:

1) \((a + 2)^3\)
\((a + 2)^3 = a^3 + 3a^2 \times 2 + 3a \times 2^2 + 2^3\)
\(= a^3 + 6a^2 + 12a + 8\)

2) \((2 + 3x)^3\)
\((2 + 3x)^3 = 2^3 + 3 \times 2^2 \times 3x + 3 \times 2 \times (3x)^2 + (3x)^3\)
\(= 8 + 36x + 54x^2 + 27x^3\)

3) \((2x + 3y)^3\)
\((2x + 3y)^3 = (2x)^3 + 3 \times (2x)^2 \times 3y + 3 \times 2x \times (3y)^2 + (3y)^3\)
\(= 8x^3 + 36x^2y + 54xy^2 + 27y^3\)

4) \((3x + 2)^3\)
\((3x + 2)^3 = (3x)^3 + 3 \times (3x)^2 \times 2 + 3 \times 3x \times 2^2 + 2^3\)
\(= 27x^3 + 54x^2 + 36x + 8\)

5) \((x + 1)^3\)
\((x + 1)^3 = x^3 + 3x^2 \times 1 + 3x \times 1^2 + 1^3\)
\(= x^3 + 3x^2 + 3x + 1\)

6) \((x + 4)^3\)
\((x + 4)^3 = x^3 + 3x^2 \times 4 + 3x \times 4^2 + 4^3\)
\(= x^3 + 12x^2 + 48x + 64\)

7) \((3x + 1)^3\)
\((3x + 1)^3 = (3x)^3 + 3 \times (3x)^2 \times 1 + 3 \times 3x \times 1^2 + 1^3\)
\(= 27x^3 + 27x^2 + 9x + 1\)

8) \((5x + 1)^3\)
\((5x + 1)^3 = (5x)^3 + 3 \times (5x)^2 \times 1 + 3 \times 5x \times 1^2 + 1^3\)
\(= 125x^3 + 75x^2 + 15x + 1\)

9) \((x + 3)^3\)
\((x + 3)^3 = x^3 + 3x^2 \times 3 + 3x \times 3^2 + 3^3\)
\(= x^3 + 9x^2 + 27x + 27\)

10) \((2x + 1)^3\)
\((2x + 1)^3 = (2x)^3 + 3 \times (2x)^2 \times 1 + 3 \times 2x \times 1^2 + 1^3\)
\(= 8x^3 + 12x^2 + 6x + 1\)

11) \((x + 3y)^3\)
\((x + 3y)^3 = x^3 + 3x^2 \times 3y + 3x \times (3y)^2 + (3y)^3\)
\(= x^3 + 9x^2y + 27xy^2 + 27y^3\)

For the expressions using the subtraction formula \((A - B)^3 = A^3 - 3A^2B + 3AB^2 - B^3\), based on the provided pattern, you or someone else might want me to expand these as well, but no specific expressions were listed for this part. If you have particular expressions to expand using the subtraction formula, please provide them!