The two numbers that, when added together, make a cube number are D. 27 and 54.
To see this, we can find the cube root of each of the numbers in the options and see which ones add up to a whole number. The cube root of 3 is slightly less than 1, the cube root of 22 is slightly more than 4, the cube root of 14 is slightly less than 3, the cube root of 16 is slightly less than 4, the cube root of 26 is slightly less than 4, the cube root of 38 is slightly more than 4, the cube root of 27 is 3, and the cube root of 54 is slightly more than 5. Only the cube roots of 27 and 54 are whole numbers, so the correct answer is D. 27 and 54