Given that the plain text(P) and the ciphertext is known, and there's a random string(8 bytes)(S) concatenated to the plain text(P || S), how to go about figuring out the random string. Querying of black box is unlimited.
Suppose you've let the box encrypt 'AAAAAAAx' for all byte values of x. (It will be the first block of the total output). Then send AAAAAAA and see what the first block is. You know now what last byte is and it's the first one of S. Now you know one byte. Think and iterate.