Yes you should convert your first output before feeding it back in: A hash function is typically a function which takes in an array of bytes (of arbitrary size) and spits out an array of bytes (of fixed size). When making the first call first = sha256('myfirstSHA'), it is likely that the string argument is implicitly converted to an array of bytes, whereby each character is substituted by a single byte encoding. However, the string output you are getting (which is a string, not an array of bytes), clearly represents a hex encoding of a 32 bytes array. You need to convert this hex encoding into a 32 bytes array. If you have a Linux terminal, as indicated by this post, a very useful command is xxd -r -p which converts your hex encoding into actual bytes:
$ echo -n myfirstSHA | sha256sum
9b2b95b24dd9149480ebda21aafe3f1a3c0370798ceec3c4d09c6a16adfe01c8 -
$ echo -n myfirstSHA | sha256sum | xxd -r -p | sha256sum
96082208e341446bb8ba032486d142cbe73f1a66276b96c18ff815f31293fe0d -
If you are worried about the trailing '-' which appears in the output of sha256sum, you can cut it out:
$ echo -n myfirstSHA | sha256sum | cut -d' ' -f1
9b2b95b24dd9149480ebda21aafe3f1a3c0370798ceec3c4d09c6a16adfe01c8
and then proceed as before:
$ echo -n myfirstSHA | sha256sum | cut -d' ' -f1 | xxd -r -p | sha256sum
96082208e341446bb8ba032486d142cbe73f1a66276b96c18ff815f31293fe0d -
In case you do not trust that xxd -r -p does the right thing, you can store the output in a file:
$ echo -n myfirstSHA | sha256sum | xxd -r -p > temp
then use hexdump -C temp or indeed xxd temp to check the content of the binary file:
00000000 9b 2b 95 b2 4d d9 14 94 80 eb da 21 aa fe 3f 1a |.+..M......!..?.|
00000010 3c 03 70 79 8c ee c3 c4 d0 9c 6a 16 ad fe 01 c8 |<.py......j.....|
00000020
