Draw a big ASCII X

MATL, 16 bytes

EQXyG:Y+tP+g42*c

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Explanation

Consider input 2 as an example. Stack contents are shown with more recent ones below.

EQ    % Implicitly input n. Push 2*n+1
      %   STACK: 5
Xy    % Identity matrix of that size
      %   STACK: [1 0 0 0 0;
                  0 1 0 0 0;
                  0 0 1 0 0;
                  0 0 0 1 0;
                  0 0 0 0 1]
G:    % Push [1 2 ... n]
      %   STACK: [1 0 0 0 0;
                  0 1 0 0 0;
                  0 0 1 0 0;
                  0 0 0 1 0;
                  0 0 0 0 1],
                 [1 2]
Y+    % 2D convolution, extending size
      %   STACK: [1 2 0 0 0 0;
                  0 1 2 0 0 0;
                  0 0 1 2 0 0;
                  0 0 0 1 2 0;
                  0 0 0 0 1 2]
tP+   % Duplicate, flip vertically, add
      %   STACK: [1 2 0 0 2 1;
                  0 1 2 1 2 0;
                  0 0 1 4 0 0;
                  0 1 2 1 2 0;
                  1 2 0 0 1 2]
g     % Convert to logical
      %   STACK: [1 1 0 0 1 1;
                  0 1 1 1 1 0;
                  0 0 1 1 0 0;
                  0 1 1 1 1 0;
                  1 1 0 0 1 1]
42*   % Multiply by 42.
      %   STACK: [42 42  0  0 42 42;
                   0 42 42 42 42  0;
                   0  0 42 42  0  0;
                   0 42 42 42 42  0;
                  42 42  0  0 42 42]
c     % Convert to char. Char 42 is '*'. Char 0 is displayed as space
      %   STACK: ['**  **';
                  ' **** ';
                  '  **  ';
                  ' **** ';
                  '**  **']

Charcoal, 13 12 bytes

Thanks to @ErikTheOutgolfer for a byte

ＦＮ«ＰX⁺*×*Ｉθ→

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This is my first ever Charcoal answer, and I'm pretty sure it's not golfed as well as it could be, but I figured I'd start somewhere.

 ＦＮ«            # For input() (i in range(0,input()))
     Ｐ           # Print
       X          # In an 'X' shape
        ⁺*×*Ｉθ   # '*'+'*'*int(first_input)
               →  # Move the cursor right one

Jelly, 15 bytes

Ḥ‘Ḷ⁶ẋ;€”*ẋ$»Ṛ$Y

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