a(n) is the number of cubes with at most n digits and first digit 1.

Terms

a(0) =1a(1) =1a(2) =2a(3) =5a(4) =11a(5) =23a(6) =49a(7) =105a(8) =225a(9) =485a(10) =1045a(11) =2252a(12) =4852a(13) =10452a(14) =22517a(15) =48510a(16) =104508a(17) =225153a(18) =485075a(19) =1045058a(20) =2251505a(21) =4850716a(22) =10450546a(23) =22515012a(24) =48507117a(25) =104505409a(26) =225150073a(27) =485071123a(28) =1045054049a(29) =2251500692