Given the key, the plain text and the cipher text can I calculate the IV used in CBC mode?
It is simple.

Just decrypt first 8 bytes encrypted buffer(1 block) in ECB mode (You only need encrypted buffer and key to do so) and then xor the result with the input buffer. Result will be IV.

In decryption of CBC, IV just affect first block. That's why only first block is incorrect in your case.