Let's break down the expression step by step:

1. Start with the innermost parentheses:
\[
35_{21}:3
\]
This notation is a bit unclear, but assuming it means division:
\[
35 \div 3 \approx 11.6667
\]

2. Next, multiply by 4:
\[
4 \times 11.6667 \approx 46.6667
\]

3. Subtract this result from 178:
\[
178 - 46.6667 \approx 131.3333
\]

4. Now, divide 330 by this result:
\[
330 \div 131.3333 \approx 2.512
\]

5. Finally, multiply by 31:
\[
31 \times 2.512 \approx 77.872
\]

So, the result of the expression \(31 \times \left( 330 \div (178 - 4 \times (35 \div 3)) \right)\) is approximately \(77.872\).