You can get all fancy and use a true panoramic photograph and manipulate the projection at the top and bottom. While I would like to learn how to do this, for now I can just choose photos that are "good enough".
How to make a panoramic photo cube
Choose an appropriate photograph. It needs to be in landscape orientation with the visual interest right across the center. (Envision a grid 3 squares tall by 4 squares wide. The center third is what you will see going around the cube).
Compare the "viewing window" on these two photos. You can see that the top photo works better than the bottom one.
Open your photograph in an editing program and resize it. You want the proportion of the height to width to be 3:4. I used 7.5" high and 10" wide. You can see on the photo (above) that I would need to cut off the far right-hand edge. That's okay! Move your grid around until you find the most pleasing part of the photo.
Add tabs at either side of the center of the photo. I filled mine with color to make them less noticeable in the finished cube.
Print and cut out photo, cutting around tabs.
Flip over to backside. Cut slits in tabs as shown, creating a slot on one side and a tab with ears on the other.
Measure off the 12 block grid. (In mine, they are 2.5" square.) Score and crease.
Score diagonal lines across the bottom 4 blocks and the top 4 blocks. Crease.
Fold in the ears of the tab. Curl the cube into a tube and insert the tab into the slot. Unfold the tabs on the inside of the cube.
Assemble the top. Fold like an origami Fujimoto cube (except we have removed one row of the grid).
Fold the bottom in the same way.