Is there any difference between nevertheless and never the less?

Solution 1:

Nevertheless is a conjunctive adverb:

: in spite of that : however <her childish but nevertheless real delight — Richard Corbin>

—source Mirriam Webster

Never the less is probably a typo. When it appears as three separate words, it means something quite different. One valid way of using this three-word phrase would be:

You should always select the container that is more full, never the less.

A quick Google NGram search shows that never the less is quite rare.