I was working on this logo today, and needed a simple isometric cube as a starting point.
Typically I'd go through the hassle of making an isometric grid, but if all you need is a cube, then there is a much quicker way. Don't worry, I'll show you how.
So, here goes... Fire up Adobe Illustrator and create yourself a new document. I'll assume you know how to do this, so once you have a blank page in front of you, you're ready to go.
Select the star tool from the shape menu in the tool box which is usually on the left hand side of the screen. Once selected, click once anywhere on the artboard.
A menu box will appear. Make sure that you have the same measurement in the boxes 'Radius 1' and 'Radius 2'. I used 20mm, but it could be any measurement you fancy. Just make sure they're the same.
The next thing you need to do is reduce the number of points to 3. (Don't ask me why, it just works).
It should look something like the below, but may be in a different colour, depending on what was selected on your document.
The next step is to select the shape, press Command/Ctrl+C to copy, and then Command/Ctrl+F to paste in front.
With 'snap to point' enabled, click and drag the uppermost point of the new shape and move to the position shown below.
This should 'snap' precisely into place. If not, go to your 'View' menu on the top toolbar and make sure 'snap to point' is enabled.
Copy and paste this shape (command/Ctrl+C then Command/Ctrl+F) and then using the upper-most anchor point, drag the new shape to the position shown below.
Press Command/Ctrl+A to 'select all' and then press the 'divide' button in the pathfinder palette.
(Make sure you have this visible by going to 'Window' in the top toolbar and going down to 'Pathfinder', it should have a tick next to it).
What this does is separate all the different overlapping sections into individual shapes. I've highlighted in blue the two pieces you need to remove.
Be sure to un-group the selection first. You can do this by selecting all the shapes, going to the 'Object' menu on the top toolbar and selecting 'ungroup'.
You now have a perfect Isometric cube. Each face is selectable, so you can change the fill colour or the stroke to whatever you like... All that is left now is to use this to create something awesome of your own.