Solve the cubic equation using factoring and the quadratic formula.
\[
x^{3}+1000=0
\]

Step 1 ：Understand the problem: The problem is asking us to solve the cubic equation \(x^{3}+1000=0\).

Step 2 ：Rearrange the equation: We can rearrange the equation to isolate the cubic term on one side of the equation. This gives us: \(x^{3} = -1000\).

Step 3 ：Take the cube root of both sides: To solve for x, we take the cube root of both sides of the equation. This gives us: \(x = \sqrt[3]{-1000}\).

Step 4 ：Calculate the cube root: The cube root of -1000 is -10. Therefore, the solution to the equation is: \(x = -10\).

Step 5 ：Check the solution: We can check our solution by substituting x = -10 back into the original equation: \((-10)^{3} + 1000 = -1000 + 1000 = 0\). Since the left-hand side equals the right-hand side, our solution is correct.

Step 6 ：\(\boxed{x = -10}\)