Beginner Hoiloilo made a video beating Cube Roll with 664 moves on September 14th, 2020. The route saves 2 on Level 15, 1 on Level 18, and 1 on Level 20. Thanks to Cocoamallows for the 668 guide.

1. DR5 6
2. D3R3U3LULU2R2DR2U2R2D6L2U2 33
3. DLURDR 6
4. U2LDRDR3U2L 12
5. U2LDRDR2URUL 12
6. LD3RURUR2ULD4RURDRU 22
7. D4R7D3L3U3 20
8. U2R2D2R2U2R2U4L5 21
9. DRD2RD 6
10. R4U2LURDR2U4L5D2L2 25
11. R2U5R2LD3L 13
12. D2R5U5L2DL3UL2D7R7L7U7R2DR3UR2D5L5U2R3 73
13. D3R6U2D2L6U6R6D2U2L6D3R3ULD2RUR 54
14. D2ULU2R5LRLDLD2UDUDUD2RU2RD 30
15. ULDR4DUDL3D2RU 17
16. UDRLDRUL3UDR2D2L3UL2 22
17. LDRU2R6DLDL3DRULD3R3URD2L2DL5UDR5UR2U2LDL3U3RDLUR3URUL6DRU 78
18. DR5L2D2RD2LU2L2D2RLRU2RU2RU2D2LD2LD2LRU2L2D3L 49
19. D2LD2LURURU2R2D3RD2L2UDR2U2LU3L2D2LDLD3RDR6ULDL5ULU3RURU2L2DUR2D2LD2LD2RDR5URU4LRD5L6ULU2RULDRU2RU2R5 127
20. RDRLRL3D3RU2DU2RLD4U2RLR2D2LDR3LU 38

Total: 664

Source video