A155986 a(1), then a(n) = smallest cube not occurring earlier, not ending with zero and starting with the last digit of a(n-1).

1, 125, 512, 27, 729, 9261, 1331, 1728, 8, 85184, 4096, 64, 4913, 343, 3375, 5832, 216, 6859, 91125, 50653, 32768, 804357, 74088, 830584, 42875, 54872, 2197, 79507, 704969, 97336, 68921, 10648, 857375, 59319, 912673, 35937, 753571, 12167, 778688