Yes, CY3210-PSoC Eval1 board can be used to program 8 pin and 20 pin packages as well but with some modification because the routing of the Vdd and Vss lines on the board is done according to the 28 pin package.
Modifications for 8 pin package:
1. Connect P1 on J6 to VDD on J5. This will connect Pin no.18 of 28 pin package to VDD. Remember to remove the jumper from JP1. This jumper connects P1 to the RS232 transceiver.
2. Place the 8 pin package pin no. 4 into pin no. 14 of 28 pin package.
Modifications for 20 pin package:
1. Place a wire jumper between P0 on J6 to VDD on J5. This will connect Pin 24 of the 28 pin socket to VDD.
2. Place the 20 pin package pin no.10 into pin no.14 of 28 pin package.
Note that the ISSP line for 8 pin, 20 pin and 28 pin are at the same location with reference to Vss. Thus aligning the VDD pin will be enough.