1. The problem states that the net of a cube is shown on the coordinate plane, and we need to find the surface area of the cube in square units. 2. A cube has 6 faces, all of which are squares of equal side length. 3. From the description, each small square in the net has vertices that differ by 1 unit in both x and y directions, so the side length of each square face is $1$ unit. 4. The surface area $S$ of a cube with side length $s$ is given by the formula: $$S = 6s^2$$ 5. Substituting $s=1$ into the formula: $$S = 6 \times 1^2 = 6$$ 6. Therefore, the surface area of the cube is $6$ square units.