So, it looks like you have more input points than grid cells. Do you even need to compute a density? Just compute the cell coordinates for each point, summarize the point data by cell, and convert that directly to a grid.
A density calculation amounts to a smoothing of this grid. ArcGIS can't handle it mainly because it uses an algorithm designed for a relatively small number of input points, not an entire grid of them. There is another algorithm though, using Fast Fourier Transforms, that will do the job and--amazingly--it will be faster in processing your 54 million points than Spatial Analyst will in processing just a few hundred points. (You will need a few seconds of CPU time, a few seconds of disk I/O, and about 100-200 MB RAM.) That's the good news. The bad news is that you have to use other software. Idrisi will do it and so, with some effort, will GRASS. Just about any decent image-processing software will also do it, albeit at some loss in the resolution of the grid values.