Answer:

To determine if a number is the cube of an odd integer, we need to find the cube root of that number and check if it is an odd integer.

Let's find the cube roots of the given numbers:

1. Cube root of 1000 = 10 (10 * 10 * 10 = 1000)

  10 is an even integer, not an odd integer.

2. Cube root of 6859 = 19 (19 * 19 * 19 = 6859)

  19 is an odd integer, so 6859 is the cube of an odd integer.

3. Cube root of 531441 = 27 (27 * 27 * 27 = 531441)

  27 is an odd integer, so 531441 is the cube of an odd integer.

So, out of the given numbers, 6859 and 531441 are the cubes of odd integers.

Step-by-step explanation: