There are 4 objects, "keys", that can be constructed from the pieces of these puzzles. The keys are made from assemblies of 28 cubes. One resembles a two basin sink; the other three are 3x3x3 arrays with an extra cube added at one of three different places.
Three puzzles are given; sets of 4 different 7-cubes. If a single puzzle is sufficient set1 prints most readily - see printing instructions. Set3, which contains a mirror pair, is probably the most difficult to solve.
OpenSCAD code is included.
The keys can be printed in draft mode without support. One piece in each of the puzzles has a cube face that needs support. The face in set1 is supported on 2 sides - a bridge. If printing software supports bridges set1 can be printed in draft mode without support.
A tiling search was used to construct these puzzles see - tiling-04.tar at - http://djm.cc/dmoews.html - If all the sorting and comparisons necessary were done correctly there are 6 sets of four 7-cubes that assemble into the 4 keys. These six answers contain 15 different 7-cubes. Three of the 7-cubes occur four times - paired so that two occur in each of the six sets. The remaining 12 7-cubes are all unique, two for each of the six answers. Seven sets of mirror images make up 14 of the 15 pieces - the remaining piece is symmetric and superimposes on its mirror image. View_pieces.scad shows images of all the pieces.
The three puzzles presented here are mirror images of a second set of three puzzles. The openSCAD code constructs all of the pieces. View_answers.scad shows all possible solutions for set1, set2, and set3 - note that some are symmetry related. The image below shows single solutions for set1.