Which number should come next in the series 1, 8, 27, 64, 125, 216, ______ so that the sequence follows the same pattern?

Introduction / Context:
This question is a straightforward number series based on powers of integers. You are given a sequence of positive integers and must identify the next term by recognising the pattern. Such questions evaluate your familiarity with perfect cubes and perfect squares, as well as your ability to match each term to a simple mathematical rule.

Given Data / Assumptions:

• Sequence: 1, 8, 27, 64, 125, 216, ?
• All numbers are positive integers.
• We expect a simple and consistent pattern, likely involving powers of small integers.

Concept / Approach:
A quick look suggests that these numbers are cubes. We check whether each term corresponds to n^3 for some integer n. If this is confirmed, then the next term should be the cube of the next integer in the sequence. The approach is to compute cube roots mentally or by recalling common cube values, then confirm the pattern and extend it by one more term.

Step-by-Step Solution:
Step 1: Recognise that 1 is 1^3. Step 2: Verify that 8 is 2^3, 27 is 3^3, and 64 is 4^3. Step 3: Check that 125 is 5^3 and 216 is 6^3. Step 4: Therefore the sequence can be written as 1^3, 2^3, 3^3, 4^3, 5^3, 6^3. Step 5: The next term must naturally be 7^3. Step 6: Calculate 7^3 = 7 * 7 * 7 = 49 * 7 = 343.

Verification / Alternative check:
To verify, confirm that no other pattern among the options fits as neatly. All given numbers are exactly cubes of consecutive integers, and only 343, which is 7^3, continues this rule. The other options do not correspond to 7^3 or to any obvious continuation of comparable simplicity. Since exam number series are usually based on a single clear idea, the cube pattern is the intended one and 343 is the only reasonable extension.

Why Other Options Are Wrong:
Option A (354) is not a cube of any integer and does not match 7^3. Option C (392) also does not equal 7^3 and fails to correspond to any simple power sequence consistent with the previous terms. Option D (245) is not the cube of 7 and has no direct relation to the displayed pattern. These numbers may appear close in magnitude but they do not fit the elegant n^3 structure visible in the given series.

Common Pitfalls:
A common mistake is to try differences between consecutive terms and misinterpret them as a primary rule, instead of checking for powers first. Learners sometimes overlook simple power patterns because they rush through the question. Another pitfall is confusing cubes with squares, which can lead to incorrect selections. Remembering standard cubes from 1^3 up to at least 10^3 makes such questions very quick to solve.

Final Answer:
The next term in the series is 343, so option B is correct.