Copy and paste sketch to multiples planes on a cube

Regardless of whether it's a good idea or not, I think the transform pattern custom feature should be able to do this... Although it will be a pattern of the same sketch always identical to the first one (i.e. can't be edited separately).
https://cad.onshape.com/documents/25a0a6dfaa76e64574a5e0db/v/8217d6d96ccc324b8dd86160/e/4c62c06c4e0e4db3703a2d4c

You can actually copy a sketch (right click "copy sketch") and paste it on a new face (select face and right click "paste sketch"), but you'd have to edit it to constrain it again if you want to edit it separately after. You'd have to paste it on one face at at time but it's pretty easy to do...

Here's an example with the transform pattern patterning sketch1 on some of the faces and "sketch2" being copy pasted from "sketch1":
https://cad.onshape.com/documents/46a326b4a97bd99579866e64/w/98aff52f023b0b23139beb54/e/a699a4775463f98ce0b0d693

glen_dewsbury said:

Here is a sample using arrays to repeat a sketch around a cube. I recommend extruding your feature first and arraying that. 
You can copy paste sketches as well. You'll need to transform each paste to correct position. Will not maintain geometry between sketches.
As Neil indicates, these may not be the most practical methods. 
https://cad.onshape.com/documents/65753e08aca8d4b30d6b151b/w/7c9c24eefc69c7c393e4fae5/e/ba75cf0069ceb1fe4dd92fa4

Was just looking at your example: the circular patterns do work for an exact cube (which is the OP's question) but you still need two separate features compared to the "transform pattern".
Also, I was wondering why you are creating a circular sketch (sketch2) for the pattern axis when you can just use an implicit mate connector on the center of a face instead...
You could also check the "centered" checkbox on circular pattern2 to eliminate circular pattern3