Let's simplify the expression step by step:

1. Break down the terms:
\[
15 \times 24 + 15 \times 57 + 81 \times 29 + 81 \times 56
\]

2. We can use the distributive property to factor out common terms:
\[
15 \times (24 + 57) + 81 \times (29 + 56)
\]

3. Calculate the values inside the parentheses:
- For \( 24 + 57 \):
\[
24 + 57 = 81
\]
- For \( 29 + 56 \):
\[
29 + 56 = 85
\]

4. Now we substitute back:
\[
15 \times 81 + 81 \times 85
\]

5. We can again factor out the common term \( 81 \):
\[
81 \times (15 + 85)
\]

6. Calculate \( 15 + 85 \):
\[
15 + 85 = 100
\]

7. Now we have:
\[
81 \times 100
\]

8. Finally, we perform the multiplication:
\[
81 \times 100 = 8100
\]

So, the value of the expression \( 15 \times 24 + 15 \times 57 + 81 \times 29 + 81 \times 56 \) is \( \boxed{8100} \).