Choose the odd number: 27, 64, and 125 are perfect cubes (3^3, 4^3, 5^3). One number is not a perfect cube. Identify the non-cube.

Introduction / Context:
Recognizing perfect cubes is a common categorization task.

Given Data / Assumptions:

• 27 = 3^3, 64 = 4^3, 125 = 5^3.
• 384 = ?

Concept / Approach:
Compare each entry to nearby cubes or factorize to check whether all prime exponents are multiples of 3.

Step-by-Step Solution:

Verification / Alternative check:
Locate 7^3 = 343 and 8^3 = 512; 384 lies between them and is neither.

Why Other Options Are Wrong:
They equal exact cubes.

Common Pitfalls:
Assuming “even and large” implies a cube; exact equality to n^3 is required.

Final Answer:
384 is the non-cube.