The cube takes up its entire space. Other creatures can enter the space, but a creature that does so is subjected to the cube's Corrosion and has disadvantage on the saving throw. 

You can move through a space as narrow as 1 inch without squeezing. You cannot be knocked prone. Objects that cannot fit through these spaces cannot move with you.

If a creature is on the same square as this cube, it must face a saving throw of DC passive constitution plus proficiency modifier. On a failed save, the creature takes damage relative to the cubes size. On a succeeded save, the creature takes half damage. It must take this damage every round until it escapes. The escape DC is the cubes constitution modifier.

Tiny - 1d4

Small - 2d4

Medium - 3d4

Large - 4d4

Depending on the cubes size, the cube has a set movement speed:

Tiny - 30ft

Small - 25ft

Medium - 20ft

Large - 15ft

Base constitution modifier of +2

Even when the cube is in plain sight, it takes a successful check with a DC of the players passive stealth to spot a cube that has neither moved nor attacked. A creature that tries to enter the cube's space while unaware of the cube is surprised by the cube.