There are about 236 million base pairs in the honeybee genome, and at 2 bits for each base pair* it could contain 56 megabytes of information**. There are about 950,000 neurons in its brain, each one has a copy of the entire genome. When we do the multiplication we see that the honeybee brain can hold about 52,000 Gigabytes of information!
But how fast is this information being copied? It takes a male worker bee about 20 days to reach adulthood so not counting the first cell thats a rate of about 30 Megabytes/s. Thats not so fast considering a high speed hard drive can go over 1 Gigabyte/s, and technically CD/DVD technology can copy great quantities of information even faster.
All that information is packed into a volume I estimate to be less than 8 millimeters cubed. The following is not possible, but if we could extend that density of information to the volume of a typical flash drive, 9 cm^3, the brain matter could hold 60 million gigabytes.
It turns out that all this information is more than Nature really needs. In the human genome its estimated that %98 of the DNA doesn't even code for proteins. This means that the biological cost of extra DNA is almost zero. Its so cheap, so fast and so small that more compact genomes are hardly selected for!
The human genome is even bigger than a honeybee's, I wonder how much data is in a human finger . . . if anyone can hazard a guess for the number of cells in a finger, post a comment!