And if that cube is centered on a corner, it’s going to cover half of each of the four squares connected to that corner, and a creature is considered to be affected by an AoE if at least half of its square is included in the area.
Here is the entire text from DnDBeyond, Spellcasting, Areas Of Effect:
"
Areas of Effect
Spells such as
Burning Hands and
Cone of Cold cover an area, allowing them to affect multiple creatures at once.
A spell's description specifies its area of effect, typically one of five shapes: cone, cube, cylinder, line, or sphere.
Every area of effect has a
point of origin, a location from which the spell's energy erupts.
The rules for each shape specify how you position its point of origin.
Typically, a point of origin is a point in space, but some spells have an area whose origin is a creature or an object.
A spell's effect expands in straight lines from the point of origin.
If no unblocked straight line extends from the point of origin to a location within the area of effect,
that location isn't included in the spell's area.
To block one of these imaginary lines, an obstruction must provide total cover.
. . .
Cube
You select a cube's
point of origin,
which lies
anywhere on a face of the cubic effect.
The cube's size is expressed as the length of each side.
A cube's point of origin is not included in the cube's area of effect, unless you decide otherwise.
"
Notice, the point of origin of a cube isnt necessarily on a corner of a square.
It seems, the point of origin of a 5-foot cube can be any corner or side of the "face" of the cube. But the point of origin of a 10-foot cube can be the center of the "face" of the cube or a corner or side.
The last sentence is odd, but I assume it means something like, if the cube is emanating from your finger tip, your own finger tip isnt necessarily included in the effect.