I would use the NCBI Taxonomy, where you can select a particular taxonomic domain and then switch on the counts of available genomes, publications, etc.

Go to http://www.ncbi.nlm.nih.gov/taxonomy/?term=insects

click on Hexapoda and then on the grey rectangle full of check boxes choose what you want (like genomes), and then click on the Display button. You should see the number of genomes per level of taxonomy. I agree though with Biojl that it might not be updated.

You could also take a look at the genomes available page at the EBI:

https://www.ebi.ac.uk/genomes/

I think that due to the high speed of sequencing there is no updated source. You can find some in Ensembl (Ensembl, Ensembl genomes, etc) or NCBI but not all of them are there. Some of them are uploaded but lack a publication, like the polar bear, hidden here http://gigadb.org/. There was a nice database but is not updated at all: http://genomesonline.org/cgi-bin/GOLD/index.cgi

go to NCBI BioProject https://www.ncbi.nlm.nih.gov/bioproject/limits

check Organism Groups > Insects

export the result as XML and grep the uniq Taxon-Id