How do we know that everything with mass has gravity?

All this got settled between 300 and 100 years ago.

What did you Google?

Try this: http://en.wikipedia.org/wiki/E%C3%B6tv%C3%B6s_expe...

"What experimental evidence is there for this?"

Centuries of measurement, starting with the motion of the planets.

"I am asking cos I had the idea that the attractive force of gravity could come mainly from the iron core of a planet."

But it also works for stars, which are made of hydrogen. And it works for small objects in the laboratory, which can be made of anything at all. This experiment was first done by Henry Cavendish, and I've done it myself in a freshman physics lab.

"Gravity is supposed to be reduced as you get closer to the centre of the earth due to an increasing percentage of mass being above you rather than below, but is there experimental evidence of this?"

The behavior can be more complicated than that. The calculation you're thinking of is done under the assumption that the density of earth is the same all the way to the center.

Here's some experimental evidence that gravity changes with depth, compared with a couple of theoretical models (one that you're talking about, another one with linear increasing density with depth).

http://en.wikipedia.org/wiki/File:EarthGravityPREM...

The experimental curve isn't measured directly since we can't go that deep. It's calculated from the behavior of seismic waves. And if you want to start questioning that, then there's a whole lot of physics of sound you're starting to question.

Because the object with mass has gravitational pull, and attracts other objects with mass.

You can't observe it on Earth, except in laboratories, because it's gravity is much stronger than that of a pen, for example.

In zero gravity conditions, you can observe big objects attracting other objects with their own gravity.

It's not only the Earth and planets that have gravity.

It doesn't come from Fe.

If it were because of Fe, than how could black holes be the objects in space with the strongest gravitational pull?

EDIT:

Black holes aren't theoretical.

Their existence is proved by observing stars near Milky Way center. Their orbits swing around apparently empty space.

The only thing that has enough energy to bend space-time continuum like that,while emitting no light, is incredibly dense and heavy black hole.

http://www.mpe.mpg.de/ir/GC/images/orbits3d_small....

How do you explain the motion of the earth around the sun (the sun does not have an iron or metal core)? Or the motion of moons around gas giants like Saturn and Jupiter?

The motion of stars and planets can be accurately predicted using gravitation.

Also you can directly measure the force between 2 small masses with the sensitive equipment

- see link for example.

Because according to the general theory of relativity, spacetime is curved by energy. And since mass and energy are transmutable, mass must also curve spacetime. The effect of this curvature created by mass/energy is gravity. Since it is "curved", things tend to "fall/get attracted" to it similar to a funnel. This is gravity at work.