Which of the following are cubes of odd natural numbers?
125, 343, 1728, 4096, 32768, 6859
i) 125 = 5 × 5 × 5 × 5 = 53
It’s a cube of odd natural number.
ii) 343 = 7 × 7 × 7 = 73
It’s a cube of odd natural number.
iii) 1728 = 26 × 33 = 43 × 33 = 123
It’s not a cube of odd natural number. As 12 is even number.
iv) 4096 = 212 = (26)2 = 642
Its not even a cube.
v) 32768 = 215 = (25)3 = 323
It’s a cube of odd natural number. As 32 is an even number.
vi) 6859 = 19 × 19 × 19 = 193
It’s a cube of odd natural number.