Here are five puzzles made of 4 pieces that can be assembled into a cube. The puzzles are based on a 3x3x3 cube composed of 27 subcubes. This is an extension of thing:1637199 - More Three Piece Cube Puzzles. OpenSCAD code is included.

MakerBot

MakerBot Replicator (5th Generation)

Yes

Yes

These are more challenging puzzles than the 3 piece ones. The removal of the traverse path restriction gives puzzles with more complex, "chunkier" pieces. The puzzles contain 2 pieces of 6 subcubes, a piece with 7 subcubes and a piece with 8 subcubes. It is sometimes helpful to start with the assembly of the 7 and 8 subcube pieces. Puz_6678_2223.stl is perhaps the "trickiest" to assemble.