Find the odd man out: 1, 8, 27, 64, 125, 196, 216, 343

Concept: A set of numbers is tested for a shared pattern by checking whether every term fits the same algebraic form. Here the candidate pattern is that each term is a perfect cube of a positive integer, i.e. of the form n³ for consecutive integers n.

Application: Express every term in the series in that form.

1. 1 = 13

2. 8 = 23

3. 27 = 33

4. 64 = 43

5. 125 = 53

6. 196 = 142 (not of the form n3 for any integer n)

7. 216 = 63

8. 343 = 73

So 1, 8, 27, 64, 125, 216 and 343 are exactly the cubes of the consecutive integers 1 through 7, while 196 does not fit that form.

Cross-check: the cube root of 196 is approximately 5.80, not a whole number, confirming 196 is not a perfect cube — unlike every other term, each of whose cube roots is exactly an integer from 1 to 7.

Hence, 196 is the odd man out.