In this video I show my method to solve a Gear Cube Extreme and Gear Cube Ultimate.
I came up with all the algorithms except for the first one. The first one I learned from a video on how to solve the Square-1 from 3 years ago.
Step 1 Equator Layer: 2:06
Step 2 Top Corners: 3:00
Step 3 Bottom Corners: 6:03
Step 4 Top Edges to Top: 7:46
Step 5 Edge Permutation: 10:05
Step 6 Edge Orientation: 13:38
Step 7 Gear Rotation: 16:58
Move 1 Bottom Corners Swap: R2 U D’ R2′ D R2 U’ R2′ U R2 U’ R2′
Move 2 Swap Top and Bottom Edges: (R2 U R2′ U’) x5
Move 3 Swap Top Two Edges Across: R4 U2 R4 U2
Move 4 Swap Top Two Edges Adjacent: R2 D R2′ (Move 3) R2 D’ R2′
Move 5 Orient 4 Edges: (R2 U) x12
Move 6 Rotate M layer Gears: (R2)x4
Move 7 Rotate 3 top layer 1 bottom layer gears: (R2 U) x2 (Move 6) (U’ R2′) x2
PS. It’s Permute not Permutate.