To achieve a fully white (0xffffff) background surrounding a scene you need to use a sky input texture in HDR format with brightness larger than 1.0. Here is such a texture that you can download and set in the Shapespark editor Sky tab.
With this texture the result looks like this:
With a sky texture in a low dynamic range format (JPG or PNG), tone mapping makes the background look grayish:
You could increase the camera exposure to make it white, but it will likely overexpose the model, so it is better to use a much brighter HDR background.