How you can see, on the Dimensions (metric) it says my cube is 2x2x2 but on the Scale tab it is 1x1x1. How can I set it so, that the metrics are same as dimensions?
Scale is a ratio, so it don't have units. You can think of it like the "1/24" (or whatever scale) of a scale model. There is nothing wrong to have a Scale that is different of the Dimensions.
However, if you absolutely want the Dimensions to fit the Scale, you can go in Edit mode and reduce the whole cube by a factor of 2 (S / 0.5). That's pretty much useless, because if you extrude some faces, or move them, the Dimensions won't fit the Scale anymore.