First things first, Space Engine can export any scene as a 360 cubic panorama, or one made from 6 square cube facets. All you need to do in order to do that is to find a good scene in Space Engine, line up the horizon line (if there is one) by hitting the "1" key on the keypad, then hit "esc" to pull up the main program menu. From here, select "edit", and then select "Export sky box".
You will likely want to export these images as PNG files to reduce quality loss. You can also double the size from 1024 x 1024 to 2048 x 2048, but don't resize to anything but a 100% increase each time, or the export will fail. This will take a while, so be patient. Do not hit "stop", until the "export" button is no longer greyed out. Once those 6 images are complete, you will likely have to edit them in an image editor like Paint Shop, Photoshop, or Gimp. You will likely want to boost the color brightness/contrast by about 25/30, and the color saturation by about 40%, to get nearly the same thing you're seeing in the program. You won't be seeing things like bloom, lens flare, ambient brightness, etc. that are after effects, and not represented in 360 renderings, sadly.
Find these 6 images in your program directory, in the "Export" folder, and put them into your image editor so that they line up correctly. What's directly in front of you should be "Z", but it likely won't be. Decide what's "front", and then rename the files to match that. You may have to rotate the top and bottom to match the shift in "front" orientation, just rotate them in opposite directions. When they all line up properly, they should look like this:
Now rename the center square "front", and do likewise for the left, right, back, up, and down cube facets.
Now we need to turn those 6 cube faces into one image, so grab this program. It has an unlimited demo period, and watermarks the results, but since we're just transferring one data type to another one, it's free, and there's no watermark. Just open it, hit the "select input" button, select "cube faces" as the input type, and input each cube face that you just edited and renamed. Once this is done, hit "OK". Now, 2 buttons down from where you selected the input type, select "Convert Input". Select "equirectangular" (should be the default), select the output type, and hit "Convert".
Now your panorama should look like this:
Once you have achieved that, open it in this 360 panorama viewer.
Now let's see yours!