I've modded a few puzzles since I started this year, and I used the same method for all the puzzles that are done by cutting, filling and sanding only. It's works pretty well for me and produces good looking results. Since I've taken pictures at every step, I figured I'd create a simple tutorial in the hopes it might be useful

Step 1: Get a cube
Type A DIY cubes are affordable and work great for mods:


Step 2: Cover the entire cube with Scotch tape and mark your cuts
I prefer 3M gift wrapping tape. It doesn't stretch and doesn't leave much glue residue after it's removed. The advantage of covering the cube with tape is that it prohibits the cube from moving while cutting, and it allows the use of a Sharpie to mark the cuts without risking staining the plastics with the Sharpie:

This is a fairly common modification I have seen a few times in the forums. However, I can't recall what this particular puzzle is called. If someone can enlighten me, I would appreciate it.

Step 3: Cut the cube and sand the cuts
A small hacksaw works best to cut. Cut to about 0.5mm away from the markings and use a course grit sandpaper (150 or so) on a flat surface to sand the cuts down to the markings. Thanks to the scotch tape, the cube is stable and nothing should move:


Step 4: Optional: plug the holes before filling
The cube I used for this mod has edge pieces that are open in the back, i.e. they need to be closed before the pieces can be filled with Apoxie Sculpt. I use plumbers teflon tape to pack the pieces. It is thin and can be packed very tightly. Teflon also does not adhere to Apoxie Sculpt, and thus, the teflon tape can very easily be removed after the Apoxie Sculpt cures:


Step 5: Fill with Apoxie Sculpt
Fill all the pieces with Apoxie Sculpt and let cure overnight. Since the cube is covered with scotch tape, it is ok for Apoxie to get on the other pieces:


Step 6: Sand the cube
While the cube is still assembled, use sandpaper on a flat surface and grind the cube against it to sand down the Apoxie Sculpt. Start with a course grit and move up to finer and finer grit until the all the sculpt is sanded down to the markings and all surfaces are flat and smooth:


Step 7: Disassemble the cube and remove the teflon tape
Before taking the cube apart, sand fillets onto all the edges of the sanded surfaces where possible:


Step 8: Sand fillets to all sharp edges and assemble the cube
Sand fillets to all the edges that have not been sanded down yet and put the cube back together:


Step 9: Cut and apply stickers
If the stickers are cut right and the mod allows it, it may not be necessary to paint the cube. The stickers will cover the sculpt nicely:


Step 10: Enjoy your new puzzle

Well made tutorial.

A common problem is to make cuts equally precise.
You achieve this by precise markings?

Thank you. This tutorial is really helpful.

Hopefully now I can start modding over the 25 cubes I need to mod!

Yes. Another advantage of covering the cube with transparent tape that doesn't stretch is that you can mark in places where normally you couldn't, e.g. in the gaps between pieces. I also use a caliper to find the vertexes of the markings before I use the sharpie to draw them. By carefully sanding down to the markings I get pretty good precision. I attach sand paper to a very flat surface (I have a laminated piece of particle wood that is very flat), and I grind the cube against the sand paper to ensure I create a flat surface on the cube