a(1) = 1, a(n+1)= smallest cube greater than the n-th partial sum.

Terms

a(0) =1a(1) =8a(2) =27a(3) =64a(4) =125a(5) =343a(6) =729a(7) =1331a(8) =2744a(9) =5832a(10) =12167a(11) =24389a(12) =50653a(13) =103823a(14) =205379a(15) =421875a(16) =830584a(17) =1685159a(18) =3375000a(19) =6751269a(20) =13481272a(21) =27000000a(22) =54010152a(23) =108531333a(24) =217081801a(25) =433798093a(26) =868250664a(27) =1736654408a(28) =3477265875