Number series – perfect cubes of even integers (one typographical outlier present): 8, 64, 216, 516, 512, 1000, 1728, ? Treat “516” as an obvious typo for 512 and continue the even-cube pattern.

Introduction / Context:The list clearly points to cubes of even integers: 2^3=8, 4^3=64, 6^3=216, 8^3=512, 10^3=1000, 12^3=1728. The “516” entry is a common transcription slip for 512 and does not alter the intended pattern.

Given Data / Assumptions:

• Even integers in order: 2, 4, 6, 8, 10, 12, …
• Series terms are the cubes of those integers.

Concept / Approach:After 12^3, the next even integer is 14; compute 14^3.

Step-by-Step Solution:

Verification / Alternative check:Neighbor terms 1000 (10^3) and 1728 (12^3) confirm the “even cubes” interpretation; 2744 (14^3) continues it cleanly.

Why Other Options Are Wrong:

Common Pitfalls:Being thrown off by the single mistyped 516; always check nearby perfect powers before rejecting a pattern.

Final Answer:2744