adriftcube

I managed to find a cheat album on Google+ I used to reconstruct the original 45 levels.  In these solutions, from time to time I would see a rainbow spinner tile that seemed to work like a wildcard; I don't know if the wildcard exists on the cube, so I separated the stages that have it into a second table.

Level 1) 3_CL00T20_CT02R11_XR01_XL12_XT10_XT11_XT12
Level 2) 3_CL11R20_CL22R21_XR00_XR01_XR02_XT20
Level 3) 3_CL00R02_CL01R11_CT00T02_XL11_XT01_XT11
Level 4) 3_CL00R20_CL12R21_CT20R22_XR01_XR02
Level 6) 3_CL00R02_CL10L22_CT01L20_CT02R00
Level 7) 4_CL00T33_CL10R30_CL20R03_CR01R33_XL33_XT30
Level 8) 4_CL00R03_CL11R32_CR02T03_CR21T12_XT10_XT11_XT22_XT32_XL21_XL31_XR01_XR11
Level 9) 3_CL10L22_CL20T10_CT02R20_XR11_XR21
Level 10) 4_CT00T20_CT10L11_XL03_XL13_XL23
Level 11) 4_CL00L31_CL22R30_CT03R31_CR03T12_XL10_XL11_XL12_XR10_XR11_XT11_XT32_XT33
Level 12) 6_CL40T40_CT01R01_CL15R50_CR15R51_XL11_XL21_XL31_XL41_XL12_XL42_XL13_XL43_XL14_XL24_XL34_XL44_XR11_XR21_XR31_XR41_XR12_XR42_XR13_XR43_XR14_XR24_XR34_XR44_XT11_XT21_XT31_XT41_XT12_XT42_XT13_XT43_XT14_XT24_XT34_XT44
Level 13) 5_CL11T31_CT04T32_CL32T22_CR40T21_XT40_XL44_XR04
Level 14) 4_CL03T12_CT00R12_CL00R21_CL10T30_CL20T31
Level 15) 5_CL00T04_CL10T41_CL42T03_CL44T22_CL43T43_XR11_XR21_XR31_XR12_XR22_XR32
Level 16) 5_CL00R04_CT12R21_CL32R40_CT31R32_XL34_XL44_XL42_XR02_XR12_XR22_XT04_XT14_XT24_XT34
Level 17) 4_CL00T03_CL13R20_CL23R30_CT01R03_XT11_XT21_XT31
Level 18) 4_CL00L31_CL10R30_CR10T12_XL11_XL12_XR23_XT11_XT21
Level 19) 4_CL11R00_CL23T03_CT02R21_XL30_XL31_XL32_XL33
Level 20) 3_CT01L11_CT11R20_XT00
Level 21) 4_CL11R10_CL30R30_XL03_XL13_XT00_XT10_XT20_XT12_XT22_XT32_XR00_XR01_XR11_XR12
Level 22) 4_CL00T22_CL01R30_CT12L31_XL33_XR03_XR13_XR23_XT30_XT31_XT32_XR21_XR31
Level 23) 4_CL11T03_CL22T02_CL32R30_XT01_XT11_XT21_XR12_XR22_XR13_XR23
Level 25) 6_CT14L52_CT12R23_CT11R14_CL23R41_XL11_XL24_XL34_XL44_XL30_XL40_XL50_XR00_XR21_XR31_XR22_XR32_XR33_XR34_XR35_XT30_XT31_XT32_XT33_XT23_XT13
Level 26) 4_CL12R11_CT20R10_CR03R30_CT12R31_XL00
Level 27) 5_CL00R42_CL21T21_CL31T32_CT22R21_XL24_XL34_XL44_XR02_XR03_XR04_XT40_XT41_XT42
Level 28) 5_CL00L41_CL20L13_CL21T12_CT20T13_CR01R34_CT40L40_XL30_XL31_XL32_XL33_XL43_XR03_XR13
Level 29) 5_CT00T44_CL11T43_CL04L40_CL34R12_CL21R40_CR11R44_XL12_XL22_XL32_XT30_XT40_XR13_XR23
Level 30) 6_CL22R50_CL11L51_CL30R22_CL41T54_XL34_XL44_XL54_XR04_XR14_XR24_XL35_XL45_XL55_XR05_XR15_XR25_XT30_XT40_XT50_XT51_XT52_XT41_XT02_XT03_XT04_XT05_XT15_XT25_XT35_XT13_XT14_XT24
Level 31) 5_CL00L33_CL21R32_CL04R44_CR40T33_CR13R34_CR11T31
Level 32) 5_CL14R10_CL23R11_CR21R24_CR31L32_CT33R14_CT14R23_CT21T41_XL00_XL01_XL02_XL03_XL04_XT00_XT01_XT02_XT03_XT04_XL44_XR33
Level 33) 5_CT13R21_CT01R22_CR02T21_CT22L34_CR04L40_XL11_XL21
Level 34) 5_CL00R40_CL21R30_CR20T23_CT04T41_XRT0_XR02
Level 35) 4_CL11T31_CL33R30_CL03R12_CT10R11
Level 36) 4_CL11T03_CL33T11_CT00R23_CT30R31_XL12_XR11
Level 37) 5_CT01T32_CL34R31_CT41R43_CL41T23_XL11_XL12_XL13_XT20_XT21_XT22_XT13_XR04_XR03
Level 38) 4_CL00R03_CT00T30_CL21T12_CR02T33_CR12T23
Level 39) 5_CL00T40_CL12T43_CL23T24_CL41T11_CT13R40_XL13_XL14_XL10_XL32_XL42_XR02_XR12
Level 41) 5_CL00T30_CL10L42_CL11T13_CL32R22_CL41R34_CT32R31
Level 42) 5_CL00T32_CL10R21_CL22R43_CT00R31_CT10L34_XT30_XT40_XT31_XT41_XL31_XL41_XR01_XR11_XL32_XL42_XR02_XR12
Level 43) 5_CL04T41_CL12R14_CL31T04_CL33R40_CT11R11_CT21R22_XL00_XL10
Level 44) 5_CL11T43_CL41R04_CR01R33_CR11T24_CT12R03_CT40T33_CR11T24
Level 45) 6_CL11R31_CL21T25_CL31R01_CL32T15_CL24L44_CL34T34_CR05R41



Level 5) 3_CL00R00_CL10T21_CR10T11 *WILDCARD AT R02*
Level 24) 4_CL00T32_CL10R23_CL22R30_XL03_XL20_XL30_XR11_XR21_XR31_XT30_XT31_XT21 *WILDCARD AT T10*
Level 40) 5_CL00R40_CL30T40_CL40T12_CT02R21_CT13R11_XT10_XT20_XT30_XL22_XL32 *WILDCARD AT R03*