Find out next term of the series 2, 7, 28, 63, 126, ....

The differences between the consecutive terms of the series are 5, 21, 35, and 63, which correspond to the differences of consecutive cubes: 6^3 - 5^3 = 91, but analyzing the sequence values directly shows they are closely related to cubes near them. More specifically, the sequence can be expressed as n^3 + (-1)^n where n starts at 1: for n=1 it is 1 - 1 = 0 (not matching 2), so evaluating the pattern of differences reveals an alternating sign pattern where the sequence itself is formed by adding consecutive cubes. Re-evaluating the terms as differences of cubes shows 2^3 - 1^3 = 7 (second term), 3^3 + 1 = 28 (third term), 4^3 - 1 = 63 (fourth term), and 5^3 + 1 = 126 (fifth term); following this alternating pattern of subtracting and adding 1 from cubes, the next term is 6^3 - 1, which equals 216 - 1 = 215.

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