1/3 constant is related with rectangled objects.

Nope. 1/3 is for any object where:

There is a line.

Perpindicular to this line at any given point there is a shape.

This shape remains similar throughout the length of the line.

This shapes changes by a constant linear scale as it moves along the line, reaching a size of 0 at one end of the line.

This produces a 3D shape known as a pyramid or cone.

For a sphere you have (4/3)*pi, i.e. the volume is (4/3)*r^3. If you compare that to a cube, with a side length of 2*r, you will have a volume of 8*r^3 for the cube. This is a ratio of pi/6, or roughly 52%.

Just because a sphere is 3D doesn't mean you have to have pi in it 3 times.

This is just like area and length. They all only have it in there 1 time.

If you want more, then try higher dimensional spheres.

Such (repeated) evidence confims that the sphere's volume is NOT a bit more than 50% of cube's volume.

It's a bit less than 50% of cube's volume.

No, it doesn't. Firstly, you don't have repeated experiments, you have 1.

Even if you did, you are still completely ignoring any possible experiment errors involved.

You are yet to show your value contradicts known math.

In order to do so you actually need to know the experimental errors and get them low enough such that the known value lies outside.

This also includes any errors in the measurement.

The best section of the video has the cube (the relevant section of it) a mere ~155 px high, with each edge stretching across a few px.

That means each px is roughly 0.64 pp and thus each edge would be rouglhy 1.3 pp.

So when you combine 2 edges you are at an error of over 2 pp.

Far too much for you to tell the difference between 50% and pi/6.

You then have the systematic errors of the experiment (which do act against each other).

The ball must always be smaller than the cube or it wont fit. This is also seen from it wobbling. If the ball is just 4.9 cm instead of 5, your percentage drops to 0.49%, just below 50.

When you remove the ball, some water may come with it, making the ball appear larger.

Also, the ball has a mount on top which also displaces water making it larger.

You then have the question of if it is actually a cube or if it is just a rectangular prism, and if it is a sphere or an ellipsoid.

So what you actually have is an experiment with many significant limitations allowing you to see that the volume of a sphere is roughly 52%, in accordance with known math.

Meanwhile, like I said before, the pure math doesn't have this problem. It doesn't suffer from experimental error and instead provides the exact value (expressed in terms of pi) of the ratio.