n^3 − 1 pattern (consecutive cubes minus one) Find the next term: 7, 26, 63, 124, 215, 342, ( ... ).

Introduction / Context:
The series matches the form n^3 − 1 for consecutive integers n. Recognizing this lets you continue by moving to the next integer and applying the same formula.

Given Data / Assumptions:

• 7 = 2^3 − 1
• 26 = 3^3 − 1
• 63 = 4^3 − 1
• 124 = 5^3 − 1
• 215 = 6^3 − 1
• 342 = 7^3 − 1

Concept / Approach:
Next n = 8 ⇒ next term = 8^3 − 1 = 512 − 1 = 511.

Step-by-Step Solution:
Identify formula: term(n) = n^3 − 1.Compute for n = 8: 8^3 = 512.Subtract 1 ⇒ 511.

Verification / Alternative check:
Differences between terms grow roughly as 3n^2 − 3, consistent with cubic behavior. The explicit computations confirm the pattern exactly.

Why Other Options Are Wrong:
481, 391, 421, and 450 are not equal to 8^3 − 1 and do not continue the exact n^3 − 1 rule.

Common Pitfalls:
Misreading 124 as 125 (a perfect cube) and assuming cubes themselves, not “cubes minus one.” Always check each term.

Final Answer:
511