If you’re using a static mesh cube, you can’t apply different textures to it. If you want to do it in UE, go to Geometry and add a Box. Then you can apply textures to each individual face, and then just click Create Static Mesh in its details in the Brush section (you may need to press a little arrow to see advanced options).
You can’t apply textures to anything because it’s all [PBR][1] but you can apply multiple materials to the same static mesh.
In your modelling app, assign each poly a face ID - these are referred to as Element Index in UE4 and each static mesh can have multiple Named Slots associated with an element index. An example:
A mesh (be it a cube or something else) has some number of material slots. You can’t add more slots once the mesh is made, so you have to make the mesh with six different materials, that you can separately configure.
The easiest way to do this in the editor is to create a box using Geometry (CSG) rather than models.
Then select each face separately, and drag a different material to each face. You may want to change the size of the geometry and/or the UV scale such that the material fits on each side (by default I think the repeat is 2x2 on each side of the default cube geometry.)
Once it looks the way you want it, you can roll out an editor panel for the primitive Geometry and hit the “Convert to Mesh” button, and you will have a static mesh. At that point, you can build a blueprint from it, as well as re-assign whatever materials you want for each material slot, as it will have one material slot per assigned material it had when you turned it into a mesh.