I wrote this for deeps to mediums, but the concepts are the same for any size to any size:
There are a lot of options. I tend to play it by ear. The most straightforward of these options is a cutout.
Next would be to put all but five frames of mediums in the bottom box, put a second box on and let the deeps "dangle" into the bottom box where you left out the frames. Then fill that box out. later you can pull the deeps out when they don't have any brood in them. If you put them towards the outside they are more likely to not have brood. You could also cut some two by lumber to fit that empty space under the five frames. Two of them stacked would be 3" which would be correct.
You could put a five frame nuc box on top of the medium box with a board to cover the left over gap and wait for them to move down.
You can build a 3" tall, five frame wide shim and put it on one side and the deeps will hang into the medium at the right height. Cover the gap with a board again.
You can use a deep box and fill the rest out with mediums and either cut a piece of closed cell styrofoam to fill the gap or just let them build comb on down and cut it off later and tie it into medium frames.
You can cut out two frames of brood, tie them into medium frames, and put them above an excluder with the queen and wait for the rest of the brood to emerge (putting it in by one of the above "dangle" or other methods) and then pull the deeps.
But all in all, I just don't recommend a nuc if the combs are not what you want, e.g. if they are deeps and you want mediums; or they are large cell and you want small cell; or they are on Langstroth equipment and you want a DE or a Warre' or a top bar hive. Get a package instead.