The cube root of 512 is 8. To find the cube root of 512, we can use the prime factorization method. First, we can express 512 as a product of prime factors: 512 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2. Next, we group the factors in threes: (2 x 2 x 2) x (2 x 2 x 2) x (2 x 2 x 2). We can see that each group of three factors is a perfect cube of 2, so we can simplify the expression to 2 x 2 x 2 = 8. Therefore, the cube root of 512 is 8.