Is it possible to melt HDPE to a point where it has similar viscosity to engine oil? I have a few pieces of HDPE that I want to melt and cast into a cube of around  $\pu{5 cm}$ each side, similar to what one would do with cast resin.

I tried putting it into an oven and heating it to $\pu{250°C}$, where it melted, but never enough to pour it somewhere. 

Is there a viable way to melt HDPE scraps to a point where it becomes fluid, with a viscosity similar to engine oil, and retains this state long enough to pour it?
You may see a small reduction in viscosity with increasing temperature, but at elevated temperature the polymer will start to oxidize and/or undergo thermolysis. If I were trying to reduce viscosity I'd try blending in some low molecular weight polyethylene (LDPE). Not sure if you have the capability of doing this or if you could tolerate the resulting changes in property (loss of tensile strength, etc.). This reference:

https://doi.org/10.1080/03602550600609663

suggests you may need to go as high as 40%+ to get a significant change in viscosity.