1. **State the problem:** Simplify the expression $$\sqrt[3]{-2 \times (-37)} - \left[-2(-3) + 8 \times (-2) - 8 \times 2\right] + 5^2$$. 2. **Simplify inside the cube root:** $$-2 \times (-37) = 74$$ So, $$\sqrt[3]{74}$$ remains as is because 74 is not a perfect cube. 3. **Simplify inside the brackets:** Calculate each term: $$-2(-3) = 6$$ $$8 \times (-2) = -16$$ $$-8 \times 2 = -16$$ Sum these: $$6 - 16 - 16 = 6 - 32 = -26$$ 4. **Rewrite the expression:** $$\sqrt[3]{74} - [-26] + 5^2$$ 5. **Simplify the double negative:** $$- [-26] = +26$$ 6. **Calculate the square:** $$5^2 = 25$$ 7. **Combine all terms:** $$\sqrt[3]{74} + 26 + 25 = \sqrt[3]{74} + 51$$ **Final answer:** $$\sqrt[3]{74} + 51$$