3x3x3 335 Method
This method consists of solving the middle layer, followed by orienting and permuting the top and bottom layers with simple cuboid algorithms. There is parity in this method.
Step 1: Solve the middle layer using the commutators R U' R and L' U L
Step 2: OBS, Orient the puzzle so that on both opposite sides are either yellow OR white. The way you do this is with 2-look OLL on both sides. You may encounter OBS parity on this step.
Step 3: OYAW, Using the edge drop and corner drop algorithms, make one side all white and one side all yellow. If you encounter PBS parity in this step, solve it BEFORE you complete PBS, otherwise, you will have to do this step AND PBS twice.
Step 4: PBS, using the cuboid algorithms, permute the pieces on each side. You can use normal PLL for SOME cases, but for other, you must use the cuboid algorithms.
-Corner Swap: R2 U R2 U' R2 U' D R2 U R2 U' R2
-Corner Drop: R2 U R2 U' R2
-Edge Drop: R2
-Adjacent Edge Swap: R2 U R2 U R2 U2 R2 U2 R2 U R2 U' R2
-Across Edge Swap: R2 U2 R2 U2 R2 U2
-PBS Parity (Middle Layer Flip): R2 U2 F2 R2 F2 U2 R2
-OBS Parity (1 Rotated corner On Each Side): U R2 U R2 U' R2 y R U2 R' U' R' U' R' L' U2 L U L' U L
-"T" (Same as 4x4 parity): R2 U R2
-"Little Line": R2 U R2 F (R U R' U') F'
-all others are same (dot, L, line)
(Same as 4LLL)
+Pi but 1 corner is flipped wrong "IL": R U2 R' U' R' U' R' L' U2 L U L' U L y' L' U L U L' U2 L; this will lead you to OBS parity
+Weird Anti-Sune "J": L' U L U L' U2 L; this will lead you to OBS parity
+Headlights With 1 Piece Flipped Wrong "LI": R U2 R' U' R' U' R' L' U2 L U L' U L; this will lead you to OBS parity