Find the odd number out in the sequence of mostly perfect cubes: 8, 27, 64, 100, 125, 216, 343.

Introduction / Context:
This classic odd-one-out set contains well-known perfect cubes. The task is to identify which term is not a cube of a positive integer. Perfect-power recognition (especially squares and cubes) is a common aptitude skill.

Given Data / Assumptions:

• 8 = 2^3, 27 = 3^3, 64 = 4^3
• 125 = 5^3, 216 = 6^3, 343 = 7^3
• 100 is not an integer cube

Concept / Approach:
Verify each term against n^3 for small integers n. Since the neighbors match consecutive cubes (2 through 7 with a gap), the non-cube stands out immediately.

Step-by-Step Solution:
List cubes: 2^3 = 8, 3^3 = 27, 4^3 = 64, 5^3 = 125, 6^3 = 216, 7^3 = 343Compare: every term except 100 coincides with one of these cubesHence, 100 is not a perfect cube ⇒ odd term

Verification / Alternative check:
Try cube roots: ∛100 ≈ 4.64 (not integer), whereas ∛125 = 5 and ∛64 = 4, confirming uniqueness of 100.

Why Other Options Are Wrong:
27/125/343 are exact cubes and therefore fit the intended pattern.

Common Pitfalls:
Confusing 100 with the nearby cube 125; misreading 216 as 6^2 instead of 6^3 (it is 6^3).

Final Answer:
100