evenly space objects

cubsterky,

Or you may create the first square, then Effect>Distort & Transform >Transform>Move the desired number of copies first horizontally then vertically (or the reverse), in other words applying two effects, then Object>Expand Appearance; this will give you a Group of squares to colour.

It isn't clear what you want to do. If you want to make a pattern, that is a great option. But if you want all different squares to color differently, then a pattern isn't ideal. You might want to make one square and repeat it over and over again. You could make your first square, then hold down the Alt key to drag out a copy. If you hold down shift as well, it will constrain it (keep it parallel). If you then use the shortcut Ctlr/Cmd+D it will copy that square exactly the same distance as you just copied the last one and you can do that all the way across. Once you get across the entire row, select the row, hold down Alt and drag down a copy holding Shift to constrain. Then copy down using the same shortcut. There are other ways to do this, but as an instructor, this is a great way to learn some tools and how Illustrator works. You can then select any square and color as you like.

There are a few different ways to accomplish what you are describing. Creating a pattern is one way to explore. You'll find a short tutorial here How to create and edit patterns in Illustrator