Number series (perfect cubes): 1, 8, 27, 64, 125, 216, (…) Identify the next cube number that continues the sequence.

Introduction / Context:This is a classic sequence of perfect cubes. Recognizing perfect powers (squares, cubes, fourth powers) is vital in numerical series questions.

Given Data / Assumptions:

• Terms given: 1, 8, 27, 64, 125, 216.
• These equal 1^3, 2^3, 3^3, 4^3, 5^3, 6^3 respectively.

Concept / Approach:Continue the natural-number base by one and compute the cube for the next term.

Step-by-Step Solution:

Verification / Alternative check:List of cubes: 1, 8, 27, 64, 125, 216, 343, 512, … The next clearly is 343.

Why Other Options Are Wrong:

• 354, 392, 245: None are perfect cubes; they do not match 7^3.

Common Pitfalls:Confusing cubes with squares or mixing arithmetic progressions into a powers sequence. Always test simple power patterns first.

Final Answer:343