There are a range of datasets and code for experimenting with auditory cognitive decoding. Here is a selection. See also the Auditory EEG Decoding Challenge for more resources and ideas.
There are a number of experiments where the data has been published for all to use. In general these data are for auditory attention decoding: given brain waves, often EEG, figure out the relation to the audio that is heard, thus characterizing audio attention.
Spreadsheet of available data (Thanks to Simon Geirnaert)
Forest Gump MEG
Mick Cross - mTRF Toolbox