House numbers

The house numbers of three individuals A, B & C are (i) distinct from each other & (ii) lie between 1 & 99. Both these facts are known to all three individuals. B asks A, when C is not present, two questions: (i) 'Is your house number a perfect square?' (ii) 'Is your house no. greater than 50?' Assuming A's answers to be correct, B is able to infer the house number of A from the answer to the two questions given by A. A's house number, however, is not the same as inferred by B because A answered only the second question truthfully. C asks A, when B is not present, two questions: (i) 'Is your house no. a perfect cube?' (ii) 'Is your house no. greater than 25?' Assuming A's answers to be correct, C is able to infer the house number of A from the answer to the two questions given by A. A's house number, however, is not the same as inferred by C because A answered only the second question truthfully. Deduce the house numbers of the three individuals given that (i) A's house number is less than the house numbers of both B & C & (ii) the sum of the house numbers of the three individuals is a perfect square multiplied by two.