20. \( \sqrt[3]{8}+2^{3}\left[2^{2}\left(2^{3}-5\right)-4\right] \)

To solve the expression \( \sqrt[3]{8}+2^{3}\left[2^{2}\left(2^{3}-5\right)-4\right] \), we can break it down step by step. 1. First, calculate \( \sqrt[3]{8} \): \[ \sqrt[3]{8} = 2 \] 2. Next, calculate \( 2^{3} \): \[ 2^{3} = 8 \] 3. Now, calculate \( 2^{3}-5 \): \[ 2^{3}-5 = 8-5 = 3 \] 4. Then calculate \( 2^{2} \left(2^{3}-5\right) \): \[ 2^{2} \times 3 = 4 \times 3 = 12 \] 5. Now, substitute this into the expression within the brackets: \[ 2^{2} \left(2^{3}-5\right) - 4 = 12 - 4 = 8 \] 6. Now multiply this result by \( 2^{3} \): \[ 2^{3} \times 8 = 8 \times 8 = 64 \] 7. Finally, add the results from step 1 and step 6: \[ \sqrt[3]{8} + 2^{3}\left[2^{2}\left(2^{3}-5\right)-4\right] = 2 + 64 = 66 \] Thus, the final result is: \[ \boxed{66} \]