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If this earth were cube shaped would it be possible during Magellanic era using a float ship to figure out that the earth is cube shaped?

If this earth were cubed shape would it be possible for Magellan to prove that the earth is cube-shaped without going to space and looking at earth?

It might seem strange to think that earth might be shaped like a cube. Remember I am not saying perfect cube but rounded cube at the edge. Do you remember Comet 67P/Churyumov-Gerasimenko where spacecraft Rosetta landed? It was odd shaped. So couldn't earth be odd shaped other than a sphere? If Magellan had to prove what the shape of the earth is like that then would it be possible for him to prove that earth is cube-shaped using his floating ship? I just want to know if it were possible.

4 Answers
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Planet-sized cube will collapse under its own weight into a sphere. The comet you mentioned has too little mass for that (and it would become a sphere if it was liquid). Our Earth is essentially a bubble of lava, with thin solid crust. And it is the weight of the rock that turns lower levels into liquid lava.

So I will assume your cube planet is made of unrealistically strong materials that prevent a collapse (or it is a hollow artificial construct), the vertices of the cube will work like mountains, and edges -- like mountain ridges. So you cannot sail from one face to another. Instead of planet-wide ocean, you will have a lakes in the middle of each face. See Figure 1 here: https://arxiv.org/pdf/1206.3857.pdf

In fact, you might not be able to walk or fly across the edge, as earth-sized atmosphere will be nonexistent near the edges. Gas (just like a liquid) will try to form a sphere around the cube, and if there is not enough of it, the edges and vertices will stick out. In fact, you will have a ring of habitatable land on each face, between the central lake, and end of atmosphere. In fact, you can have completely different atmospheres on each face.

If you have enough gas to encase the entire cube (see Figure 3), the atmospheric pressure will be a lot higher, giving you (I think) a Venus-like hot world

People will notice the change in gravity angle as they travel towards edges (Figure 2), but they will just think that they are climbing a mountain ridge. Fog and dust in atmosphere will prevent people from seeing all the way across the face of the cube, so they will assume they live in a square-shaped valley surrounded by impassable mountains.

First proof of Earth shape was The Eratosthenes Experiment (250BC):
https://www.astro.princeton.edu/~dns/teachersguide/MeasECAct2.html
It was based on angle of the sun. On your cube, sun will have same angle with the surface. But just as Eratosthenes, your people will measure angle vs. up-down gravitational field line (see Figure 2). So exact replication of his experiment (with 2 points, North/South of each other) will lead to same conclusion: planet is round.

Repeating experiment with points East/West of each other might show that shape is not round, or doing the experiment with more than 2 points. I am too tired to figure out the angles :)

user535733's idea of measuring time between sunrize and sunset is valid, but requires a clock (renaissance technology) or lots of patience with hour-glass and more complex theoretical argument.

The "magellan" approach of travelling across faces requires oxygen tanks and breathing masks, or space rockets, or tunneling under the ridge/edge.

You can figure out whether or not your planetary body is cube-shaped by simply recording the rise/set times of celestial bodies, including ordinary sunrise/sunset, along a line of latitude.

At Earth's equator, for example, the sun and moon and stars rise about one hour later as you move 1000 nautical miles westward. The change is gradual and consistent.

On a cube-shaped planet, one entire face will have (essentially) the same rise/set times. As you move 1000 nautical miles increments westward, the sun keeps rising/setting at the same time on your clock...and then suddenly comes up six hours later after you round to the next face of the cube.

That day (or night) you transit between two faces, the change in the sky should be quite apparent to a keen observer. The sun and moon move noticeably faster or slower than usual (or perhaps backward). If you transit onto one of the polar faces, the changes will be even more apparent.

This should be (and was) readily detected, recorded, and calculated by Bronze-age societies (at the latest). For Magellanic-era sailors and technologies, the shape of the planet should be (and was) old news.

In the following I am not challenging the premise that the planet is shaped as a cube, just taking it for granted

The Earth is a cube, and there is somebody navigating on the seas direction East, until they reach the edge and move to the next face of the cube. What will they see?

Let's say they start from position A in the below picture: they see the sky limited by their local horizon, with the 3 red stars low on the horizon to the East.

This stays the same also when they are in B and check the position of the stars at the same time of the night.

When they reach C, however, they will notice that the 3 red stars are now high in their local sky, and when they travel further East the 3 red stars will be low on the horizon at West.

In this way, having knowledge of some projective geometry, they can figure out that the Earth is a cube.

Is it a gravitational anomaly which caused the planet to form into a cube, or was it a cubical structure that is held by artificial means (such as alien design)?

1- Gravitational anomaly: The inhabitants of one "side" of the cube will think the Earth is flat, and all indications will seem to confirm that. they will be unaware of the cubical shape. When they venture to the edge and look over the horizon they will see a vertical world just below them. Water will behave the same, so oceans will form part of the cube surface.

2- Cube held by an artificial structure: The gravity will pull the mantle to form a sphere but something prevents it from doing so. On the other hand, nothing will hold the oceans that way. The ocean will flow and gather at the center of each "side" forming a dome. The observers on land will see it and will think this is a water mountain amid a flat Earth. The inhabitants will still think the Earth is flat, unless they look over the edges. On the other hand, as they walk towards the edge, they will feel the ground gets steeper as if they climb a mountain. This is the same force which would otherwise make the cube collapse into a sphere and the water converge to form a dome. That's also the reason why rivers will tend to flow towards the center -- following gravity.

One thing will not change in either case # 1 or #2: Lunar eclipses. They will all indicate the Earth is cubical: The shadow of the Earth on the moon will always be the projection of a cube's shadow. The outlines of the shadow will always be straight lines with straight or obtuse angles, and never the side of a disk or a circle...

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