What natural numbers less than 750 are both perfect squares and perfect cubes?

Natural numbers that are both perfect squares and perfect cubes are perfect sixth powers, since the least common multiple of 2 and 3 is 6. The perfect sixth powers less than 750 are (1^6 = 1), (2^6 = 64), and (3^6 = 729). Therefore, the natural numbers less than 750 that are both perfect squares and perfect cubes are 1, 64, and 729.