Find the next term of the following number series – 5, 24, 61, 122, 213, 340, ?

Analysis of the Series
The series follows a pattern based on cubes minus 3, or a consistent second-level difference:

Pattern 1 (Cubes - 3):

2³ - 3 = 8 - 3 = 5

3³ - 3 = 27 - 3 = 24

4³ - 3 = 64 - 3 = 61

5³ - 3 = 125 - 3 = 122

6³ - 3 = 216 - 3 = 213

7³ - 3 = 343 - 3 = 340

8³ - 3 = 512 - 3 = 509

Pattern 2 (Difference Method):
The differences between terms are: 19, 37, 61, 91, 127.
The differences of those differences are: 18, 24, 30, 36.
The next difference is 36 + 6 = 42.
The next term in the series is 340 + (127 + 42) = 340 + 169 = 509.