The difference of the cubes of two non-negative successive integers is a square of an integer.
Find few possible pairs.

How about a general formula or evaluation algorithm
for a(n)?

(In reply to

computer exploration by Charlie)

I noticed the last numbers on each line get larger by a factor of about 13.9 each time, so I ran a similar program to investigate this more and found this factor converging to some limit -- I wonder what it is exactly? Here is the output of my program:

8 13 13

105 181 13.9230769

1456 2521 13.9281768

20273 35113 13.9282031

282360 489061 13.9282032

3932761 6811741 13.9282032