Where can the knight be in N moves?
Wolfram Language (Mathematica), 45 bytes

Because the other solution is incorrect (see Martin's comment below), so I decide to post my solution:

8~KnightTourGraph~8~AdjacencyList~#&amp;~Nest~##&amp;


Try it online!

Ultimate infix notation...

Takes 2 input, the first one is a list of numbers in range [1,64] describe the starting positions of the knight, the second one is the number of steps.

This solution relies on the extreme convenience of Mathematica builtin functions:


AdjacencyList may takes a list of vertices on its right side, and return a list of vertices adjacent to any of those, already removed duplicates and sorted.
KnightTourGraph is a builtin. Not surprise.
Nest takes arguments in order Nest[f, expr, n], which we can splat the ## over its right side as Nest[f, ##].
And finally, Mathematica parse a~b~c~d~e as (a~b~c)~d~e, so no square bracket is necessary. Without infix notation and flatten ##, it would be Nest[AdjacencyList[KnightTourGraph[8, 8], #] &amp;, #, #2]&amp;.