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Let the lengths of the three pieces be 2x, 3x, and 7x, respectively. According to the given information, 2x + 3x + 7x = 96. Combining like terms, we get 12x = 96. Dividing both sides by 12, we find x = 8. Therefore, the lengths of the three pieces are 2x = 2(8) = 16 cm, 3x = 3(8) = 24 cm, and 7x = 7(8) = 56 cm. Answer: \boxed{16, 24, 56}.