"■ "li({z]A*):,Sf*4\t3/{:+z~}%}*zN*

(to be continued)

"■ "                                " C := '■ '                                           ";
    li(                             " J := int(input()) - 1                               ";
       {                      }*    " for I in range(J):                                  ";
        z]A*                        "   T := [zip(C)] * 10                                ";
            ):,                     "   U := pop(T)                                       ";
               Sf*                  "   V := [ ' ' * len(u) : u ∊ U ]                     ";
                  4\t               "   U[4] := V                                         ";
                     3/{:+z~}%      "   C := { c : c ∊ zip(concat(u)), u ∊ U.split(3) }   ";
                              zN*  " print '\n'.join(zip(C))                              ";

CJam, 32 characters

"■ ""ᖡپ掣垲﹨밈㐲嚣龜芛⊽駻持檺"7e4b128b:c~

As below, but takes advantage of scoring by character count.

If trailing spaces are allowed, I can an additional character:

"■ ""՛ୗ䁎뽔휼ꆩ闳⾿➺⥧槲㩡郊"6e4b128b:c~

Try it online.

CJam, 38 characters

"■ "li({z]A*):,Sf*4\t3/{:+z~}%}*zWf<N*

This is a recursive approach.

If trailing spaces are allowed, Wf< can be committed, leaving a total of 35 characters.

CJam, 38 35 32 31 characters

"■ ""՛ୗ䁎뽔휼ꆩ闳⾿➺⥧槲㩡郊"6e4b128b:c~

Try it online.

Example run

$ cjam <(echo '"■ ""՛ୗ䁎뽔휼ꆩ闳⾿➺⥧槲㩡郊"6e4b128b:c~') <<< 3; echo
■ ■ ■ ■ ■ ■ ■ ■ ■ 
■   ■ ■   ■ ■   ■ 
■ ■ ■ ■ ■ ■ ■ ■ ■ 
■ ■ ■       ■ ■ ■ 
■   ■       ■   ■ 
■ ■ ■       ■ ■ ■ 
■ ■ ■ ■ ■ ■ ■ ■ ■ 
■   ■ ■   ■ ■   ■ 
■ ■ ■ ■ ■ ■ ■ ■ ■ 

How it works

"՛ୗ䁎뽔휼ꆩ闳⾿➺⥧槲㩡郊"6e4b128b:c~

converts the Unicode string from base 60,000 (6e4b) to base 128 (128b), casts to Character (:c) and evaluates the resulting string (~).

As a result, the following code gets executed:

"■ "li({z]A*):,Sf*4\t3/{:+z~}%}*zN*

(to be continued)

CJam, 38 characters

"■ "li({z]A*):,Sf*4\t3/{:+z~}%}*zWf<N*

This is a recursive approach.

If trailing spaces are allowed, Wf< can be committed, leaving a total of 35 characters.

Try it online.

CJam, 32 characters

"■ ""ᖡپ掣垲﹨밈㐲嚣龜芛⊽駻持檺"7e4b128b:c~

As below, but takes advantage of scoring by character count.

If trailing spaces are allowed, I can an additional character:

"■ ""՛ୗ䁎뽔휼ꆩ闳⾿➺⥧槲㩡郊"6e4b128b:c~

Try it online.

CJam, 38 characters

"■ "li({z]A*):,Sf*4\t3/{:+z~}%}*zWf<N*

This is a recursive approach.

If trailing spaces are allowed, Wf< can be committed, leaving a total of 35 characters.