Impact of data padding on CRC calculation

I am calculating CRC on a large chunk of data every cycle in hardware (64B per cycle). In order to parallelize the CRC calculation, I want to calculate the CRC for small data chunks and then XOR them in parallel.

Approach:

1. We divide the data into small chunks (64B data divided into 8 chunks of 8B each).
2. Then we calculate CRC's for all the chunks individually (8 CRC's in parallel for 8B chunks).
3. Finally calculate the CRC for padded data. This answer points out that the CRC for padded data is obtained by multiplying the old CRC with x^n.

Hence, I am calculating the CRC for a small chunk of data, then multiply it with CRC of 0x1 shifted by 'i' times as shown below.

In short, I am trying to accomplish below:

For example: CRC-8 on this site:

Input Data=(0x05 0x07) CRC=0x54
Step-1: Data=0x5 CRC=0x1B
Step-2: Data=0x7 CRC=0x15
Step-3: Data=(0x1 0x0) CRC=0x15
Step-4: Multiply step-1 CRC and step-3 CRC with primitive polynomial 0x7. So, I calculate (0x1B).(0x15) = (0x1 0xC7) mod 0x7.
Step-5: Calculate CRC Data=(0x1 0xC7) CRC=0x4E (I assume this is same as (0x1 0xC7) mod 0x7)
Step-6: XOR the result to get the final CRC. 0x4E^0x15=0x5B

As we can see, the result in step-6 is not the correct result.

Can someone help me how to calculate the CRC for padded data? Or where am I going wrong in the above example?

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