This requires a DM ruling
The core issue here is whether different parts of the same creature can be considered to be in different lighting conditions. Unfortunately, the rules for vision and light don't seem to provide any clear guidance here, as far as I can tell.
As DM, you might decide that for the sake of simplicity, each creature is considered to be under a single lighting condition, i.e. every creature is either in darkness (i.e. heavily obscured by lighting conditions), dim light (lightly obscured by lighting), or bright light (not obscured), and the mechanical effects of that lighting condition apply equally to all parts of the creature's body. Alternatively, you might decide that the described use of the 5-foot cube of darkness is a clever one and allow the player to use it to cover only the top half of a creature's body.
Personally, I would recommend the first ruling, because of the rules for control of space:
A creature's space is the area in feet that it effectively controls in combat, not an expression of its physical dimensions. A typical Medium creature isn't 5 feet wide, for example, but it does control a space that wide.
If you created a 5-foot cube of darkness that covers a creature from the waist up, the creature could potentially just crouch down in response and see under the cube, while remaining within their 5-foot space. Hence, a static cube floating at waist height might not be effective in blinding the creature, whereas a static cube at ground level would cover the creature's entire space, which unambiguously shrouds the creature's whole body to darkness until they leave that space.