I would like to bend in a curve the 2 faces you see in this cube?
I know I can subdivide and move the vertices in a curve but is there a way to curve a line between 2 vertices?
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You can add some loopcuts and then use proportional editing with a sharp falloff to scale it into a nice curve. Notice how changing the radius and falloff type of the proportional editing tool completely changes how the vertices are deformed.(If none of the preset falloffs are good enough, you can make a custom curve to create the exact shape you want).
There are quite a few ways to bend or curve a mesh. Speaking just in edit mode there is the Warp tool, the Bend tool, Proportional Editing, etc. (To curve an entire object I have an answer that outlines a few different methods.)
No matter what tool you choose to model this, you are going to need more geometry. There is nothing that can make a curve from one face.
I see you are going for a low poly feel. Knowing that you might want to consider triangles, instead of loops going all the way around. Now on to how to make the curved faces.
Even with all the fancy tools, I still sometimes prefer to add a circle (or cylinder) and use half of it for the curved part, it's simple and easy. In the image below I added one loopcut through center so that the triangle fan would line up (else the topology would look like the image above.) With the object in this state it is a simple matter of
removing doubles merging by distance to combine the new piece.
One interesting way to curve the end face is to use the smooth feature of the Loop Cut and Slide tool. Start by deleting the connecting faces on the top and bottom (so the loops stay on the end face). Then simply add loops CtrlR and adjust the smoothness in the Adjust Last Operation panel.
You could use the Spin tool to create the new curved faces. With the corner edge selected (circled in red in the image below) initiate the spin tool, and adjust the Angle and Steps to your liking.
First added more geometry to the end face. Select the top and bottom edge of that face, Subdivide it and bump the Number of Cuts up to 5 or so. Now select the center most edge of the newly created edges, and with Proportional Editing enabled and set to Sphere move that edge out.
PS use a mirror modifier. No need to duplicate work when both sides of the object are the same.
If you want the curve to pass through a set of known points, the shipped add-on Loop Tools > Curve will make a cubic (or a linear) interpolation for you..