I bought a 7 layer VCube and I've really enjoyed it. If you have one and you prefer to see the applet below using a vcube click here.
From what I've seen there are no algorithms specific to
the 7x7x7. You can pretty much use the same ones as for the 5x5x5, you just may need to include an additional slice in your rotations.
Below you can see what happens when you apply the 5x5x5 pattern as-is vs adapting it to include additional layers.
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Double Edge Swap 5x5x5
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Double Edge Swap 7x7x7
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PATTERNS
Below are some patterns you can make which were taken from www.randelshofer.ch. To see his notation guide see this page.
You should visit his page to view all the different patterns he has collected for various cubes.
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6 W's (or M's) Pattern
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Ancient Roman Mosaic Pattern
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