14. Since the cubes are four-digit numbers by condition, their bases are two-digit numbers. If a cube ends in the digit 8, then the base ends in the digit $2\left(2^{3}=8\right)$. In this case, the base can only be 12, since $22^{3}=10648$ is a five-digit number. Therefore, the only possibility is $12^{3}=1728$. If a cube ends in the digit 9, then the base also ends in this digit. The only possibility is $19^{3}=6859$.
14. While erasing the board in class, Ira accidentally erased three digits from the calculations of the cubes of two numbers, leaving only the unit digits - 8 and 9. Help her restore all the digits and find the numbers that were cubed.