In a certain code if 64 is written as 343 and 216 is written as 729, then how is 512 written in that code?

Observe: 64 = 4³, and 343 = 7³ = (4+3)³. Similarly 216 = 6³, and 729 = 9³ = (6+3)³. Pattern: if the number is n³, the code is (n+3)³. For 512 = 8³, the code = (8+3)³ = 11³ = 1331. Hence option (b) is correct.