6818 shaares
The VGA default palette in the 256 colour mode (Mode 13h) first has 16 color entries from CGA (which is also same as default 16-color EGA palette and the only palette for 320x200 EGA mode)
Next 16 color entries are 16 shades of gray.
And the next 216 color entries has been already mentioned; they are sets of 24 hues, in 3 different saturation values, and in 3 different brightness values. 24 × 3 × 3 = 216.
The final 8 colour entries are black, or maybe left undefined so BIOS does not overwrite them when changing modes.