Simplify: (2a + b)^3 - (2a - b)^3

To simplify \((2a + b)^3 - (2a - b)^3\), we can use the identity for the difference of cubes:

\[
x^3 - y^3 = (x - y)(x^2 + xy + y^2)
\]

Here, we treat \(x = (2a + b)\) and \(y = (2a - b)\). Applying the identity:

\[
(2a + b)^3 - (2a - b)^3 = \left[(2a + b) - (2a - b)\right] \left[(2a + b)^2 + (2a + b)(2a - b) + (2a - b)^2\right]
\]

### Step 1: Simplify the first factor
\[
(2a + b) - (2a - b) = 2a + b - 2a + b = 2b
\]

### Step 2: Simplify the second factor
Now we simplify \((2a + b)^2\), \((2a - b)^2\), and \((2a + b)(2a - b)\).

#### Expanding \((2a + b)^2\):
\[
(2a + b)^2 = (2a)^2 + 2(2a)(b) + b^2 = 4a^2 + 4ab + b^2
\]

#### Expanding \((2a - b)^2\):
\[
(2a - b)^2 = (2a)^2 - 2(2a)(b) + b^2 = 4a^2 - 4ab + b^2
\]

#### Expanding \((2a + b)(2a - b)\):
\[
(2a + b)(2a - b) = (2a)^2 - b^2 = 4a^2 - b^2
\]

### Step 3: Combine the terms
Now, we combine all the terms in the second factor:

\[
(2a + b)^2 + (2a + b)(2a - b) + (2a - b)^2 = (4a^2 + 4ab + b^2) + (4a^2 - b^2) + (4a^2 - 4ab + b^2)
\]

Simplifying:

\[
4a^2 + 4ab + b^2 + 4a^2 - b^2 + 4a^2 - 4ab + b^2 = 12a^2 + b^2
\]

### Step 4: Final simplification
Now, we substitute back into the original expression:

\[
(2a + b)^3 - (2a - b)^3 = 2b(12a^2 + b^2)
\]

Thus, the simplified expression is:

\[
2b(12a^2 + b^2)
\]