15972, 15629, 15840, 15720, 15784, 15757

Key pattern: consecutive differences follow -7^3, +6^3, -5^3, +4^3, -3^3.

• 15972 − 7^3 = 15972 − 343 = 15629

• 15629 + 6^3 = 15629 + 216 = 15845 (this should be the next term)

• 15845 − 5^3 = 15845 − 125 = 15720

• 15720 + 4^3 = 15720 + 64 = 15784

• 15784 − 3^3 = 15784 − 27 = 15757

Conclusion: the term given as 15840 is incorrect; the correct term at that position is 15845. Therefore the wrong term in the series is 15840.