To solve the expression \(36 \cdot 27 + 36 \cdot 15 - 36 \cdot 42\), you can factor out the common term \(36\):
\[ 36 \cdot 27 + 36 \cdot 15 - 36 \cdot 42 = 36 \cdot (27 + 15 - 42) \]
Now calculate the expression inside the parentheses:
\[ 27 + 15 = 42 \] \[ 42 - 42 = 0 \]
Now, substitute back into the expression:
\[ 36 \cdot (27 + 15 - 42) = 36 \cdot 0 = 0 \]
Therefore, the result of the original expression is:
\[ \boxed{0} \]