Cloud of Daggers only effects one tile if we assume everything "snaps to grid."
What is "a cube 5 feet on each side?"
Looking at the section of the PHB "Areas Of Effect" we see:
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. - PHB pg.204
In a comment you said:
The other way to look at it is if a point can have a side then it - spell has a 5ft radius. This is why I have asked this question.
Which suggests you are thinking of spheres and cubes as being similar areas of effect. When we're dealing with a 5 foot cube, there is a sphere that could be considered to be almost identical in effect, but it would have a 2.5ft radius, or a 5ft diameter. Of course, when the areas we're dealing with get bigger, the similarities decrease.
Take the image below:
The point indicated is at the center of both the cube and the sphere, and the length of one side of the cube is equal to the length of the diameter of the sphere (but the radius is only half that). While the sphere fits entirely inside the cube, there is plenty of space taken up by the cube that lies outside of the sphere's bounds. When using a 5ft grid, as the sphere/cube get larger, more and more spaces are effected by this difference, which is why I said "the similarities decrease."
If we were to say that the cube is 5 feet on each side, it would fit nicely inside one 5ftx5ft tile on a map. The area of effect of the sphere and the cube would be effectively the same if we consider that everything snaps to a grid: either one would completely effect one creature, and only one, as creatures can move through eachother's space, but not stay there.
How does this effect Cloud of Daggers?
As you said, the spell states:
You fill the air with spinning daggers in a cube 5 feet on each side, centered on a point you choose within range. - PHB pg.222
Usually you select the point of origin, which can be included in the effect or not, but in this case we select the center point, which must be within the area of effect. From this, we can see that a cube 5ft on each side could fit perfectly within one tile of a 5ft grid.
Again, in a comment you said:
we play with the notion that when you select a point you are select a square rather than a location on the grid which could cross into another square or in the middle of two.
Which sounds like snap-to-grid, so you couldn't place the cube on the intersection of two tiles as addressed by this question.
In conclusion:
Cloud of Daggers only effects one tile if we assume everything "snaps to grid."