RAD, 51 46 39 bytes

{+/(⍵∘+¨(⊖,⊢)(⊢,-)(⍳2)(1¯2))∊,W}¨¨W←⍳⍵⍵

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##How?

Counts the number of valid knight moves for each square by seeing which knight moves would land on the board:

{+/(⍵∘+¨(⊖,⊢)(⊢,-)(⍳2)(1¯2))∊,W}¨¨W←⍳⍵⍵
 +/                                     - The number of ...
                            ∊,W         - ... in-bounds ...
        (⊖,⊢)(⊢,-)(⍳2)(1¯2)             - ... knight movements ...
   (⍵∘+¨                   )            - ... from ...
{                              }¨¨W←⍳⍵⍵ - ... each square

RAD, 51 46 39 bytes

{+/(⍵∘+¨(⊖,⊢)(⊢,-)(⍳2)(1¯2))∊,W}¨¨W←⍳⍵⍵

Try it online!

How?

Counts the number of valid knight moves for each square by seeing which knight moves would land on the board:

{+/(⍵∘+¨(⊖,⊢)(⊢,-)(⍳2)(1¯2))∊,W}¨¨W←⍳⍵⍵
 +/                                     - The number of ...
                            ∊,W         - ... in-bounds ...
        (⊖,⊢)(⊢,-)(⍳2)(1¯2)             - ... knight movements ...
   (⍵∘+¨                   )            - ... from ...
{                              }¨¨W←⍳⍵⍵ - ... each square

RAD, 51 46 bytes

{+/(⍵∘+¨,(4 2⍴⌽,⊢,-,-∘⌽)¨(⍳2)(1¯2))∊,W}¨¨W←⍳⍵⍵

Try it online!

##How?

Counts the number of valid knight moves for each square by seeing which knight moves would land on the board:

{+/(⍵∘+¨,(4 2⍴⌽,⊢,-,-∘⌽)¨(⍳2)(1¯2))∊,W}¨¨W←⍳⍵⍵
 +/                                            - The number of ...
                                   ∊,W         - ... in-bounds ...
        ,(4 2⍴⌽,⊢,-,-∘⌽)¨(⍳2)(1¯2)             - ... knight movements ...
   (⍵∘+¨                          )            - ... from ...
{                                     }¨¨W←⍳⍵⍵ - ... each square

RAD, 51 46 39 bytes

{+/(⍵∘+¨(⊖,⊢)(⊢,-)(⍳2)(1¯2))∊,W}¨¨W←⍳⍵⍵

Try it online!

##How?

Counts the number of valid knight moves for each square by seeing which knight moves would land on the board:

{+/(⍵∘+¨(⊖,⊢)(⊢,-)(⍳2)(1¯2))∊,W}¨¨W←⍳⍵⍵
 +/                                     - The number of ...
                            ∊,W         - ... in-bounds ...
        (⊖,⊢)(⊢,-)(⍳2)(1¯2)             - ... knight movements ...
   (⍵∘+¨                   )            - ... from ...
{                              }¨¨W←⍳⍵⍵ - ... each square

RAD, 51 46 bytes

{+/(⍵∘+¨,(4 2⍴⌽,⊢,-,-∘⌽)¨(⍳2)(1¯2))∊,W}¨¨W←⍳⍵⍵

Try it online!

Counts the number of valid knight moves for each square by seeing which knight moves would land on the board.

RAD, 51 46 bytes

{+/(⍵∘+¨,(4 2⍴⌽,⊢,-,-∘⌽)¨(⍳2)(1¯2))∊,W}¨¨W←⍳⍵⍵

Try it online!

##How?

Counts the number of valid knight moves for each square by seeing which knight moves would land on the board:

{+/(⍵∘+¨,(4 2⍴⌽,⊢,-,-∘⌽)¨(⍳2)(1¯2))∊,W}¨¨W←⍳⍵⍵
 +/                                            - The number of ...
                                   ∊,W         - ... in-bounds ...
        ,(4 2⍴⌽,⊢,-,-∘⌽)¨(⍳2)(1¯2)             - ... knight movements ...
   (⍵∘+¨                          )            - ... from ...
{                                     }¨¨W←⍳⍵⍵ - ... each square