I believe the 29 is a typo and should have been 28, because

  1 = 0³ + 1
  2 = 1³ + 1
  9 = 2³ + 1
 29 = 3³ + 2   <--- I believe this should have been 28
 65 = 4³ + 1

Change 29 to 28, and we have:

  1 = 0³ + 1
  2 = 1³ + 1
  9 = 2³ + 1
 28 = 3³ + 1   
 65 = 4³ + 1
126 = 5³ + 1

So if 29 was a typo and should be 28, the next term is 126.

Edwin