Determine which of the following statements is/are true:

Let's evaluate each statement step by step:

### Statement #1:
\[ 3 \cdot 20 = 4(6 + 9) \]

Calculating both sides:
- Left side:
\[ 3 \cdot 20 = 60 \]
- Right side:
\[ 4(6 + 9) = 4 \cdot 15 = 60 \]

So, Statement #1 is **true**.

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### Statement #2:
\[ 4 \cdot 12 = 6 \cdot (8 \cdot 2) + 12 + 6 \cdot \sqrt{64} = 2 \cdot 4 \cdot 8 \]

Calculating both sides:
- The first part, \( 4 \cdot 12 = 48 \).

Now let's calculate the right side:
- \( 6 \cdot (8 \cdot 2) = 6 \cdot 16 = 96 \)
- \( 12 + 6 \cdot \sqrt{64} = 12 + 6 \cdot 8 = 12 + 48 = 60 \)

So,
\[ 6 \cdot (8 \cdot 2) + 12 + 6 \cdot \sqrt{64} = 96 + 60 = 156 \]

Now let's calculate \( 2 \cdot 4 \cdot 8 \):
\[ 2 \cdot 4 \cdot 8 = 64 \]

Since \( 48 \neq 156 \) and \( 48 \neq 64 \), Statement #2 is **false**.

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### Statement #3:
\[ 4 \cdot 18 - 4 \cdot 6 = 4^2 + 4 \cdot 8 \]

Calculating both sides:
- Left side:
\[ 4 \cdot 18 - 4 \cdot 6 = 72 - 24 = 48 \]

- Right side:
\[ 4^2 + 4 \cdot 8 = 16 + 32 = 48 \]

So, Statement #3 is **true**.

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### Conclusion:
The statements that are true are 1 and 3.

Thus, the answer is **1 and 3**.