8-bit Chess Pixel Counting
C#6, 107 bytes

Here's my own answer.  I don't expect any points being the one who posed the challenge.

I have taken some inspiration from user81655's answer.

long P(string a)=&gt;(a[0]&gt;99?12201284685:11042628752)+(a[2]+a[3])%2*46566348643&gt;&gt;"KQBNRP".IndexOf(a[1])*6&amp;63;


The pixel counts are encoded in 6-bit blocks.  The outline or fill is added to the square (if it's white).  Finally, the 6-bit block for the appropriate piece is extracted.

Thankfully, operation precedence worked heavily in my favor.