It’s hard

Consecutive terms are separated by prime numbers.

The first two terms differ by the $4$ th prime $(7)$ .

The next two terms differ by the $8$ th prime $(19)$

So this leaves $26$ and $63$ to differ by the $12$ th prime $(37)$ , and $63$ and $124$ to differ by the $16$ th prime $(61)$ .

Probably it was a series of cubes of subsequent natural numbers reduced by unity... Happy learning :)