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With Mathematica 10.4.1 on Windows 7 x64 I get FrontEnd crash with your code by default but switching to "Graphics3DRenderingEngine" -> "BSPTree" produces the expected output which is relatively responsible (comparing to the Image3D):

SeedRandom[10] i3d = 1/4 RandomReal[1, {5, 5, 5}] // Image3D 

Style[Show[{i3d, Graphics3D[{FaceForm[Opacity[.6]], Cuboid[{3, 3, 3}]}]}], RenderingOptions -> {"Graphics3DRenderingEngine" -> "BSPTree"}] 

The option RenderingOptions -> {"Graphics3DRenderingEngine" -> "Software"} produces the same but seems to be even slower.

An attempt to Export this as PNG with ImageSize -> {2400, 1600} crashed my video driver and I got not responding FrontEnd taking 100% CPU time of one of my cores. So at least my graphical card doesn't allow to render such a large image.

As a workaround you can try to apply an incremental rendering technique. This post of mine (see the "EDIT 4" section) shows Inset-based approach, another method is suggested by Vitaliy Kaurov (search for "3dImagePartitionExport.nb" in this Wolfram Community thread).

With Mathematica 10.4.1 on Windows 7 x64 I get FrontEnd crash with your code by default but switching to "Graphics3DRenderingEngine" -> "BSPTree" produces the expected output which is relatively responsible (comparing to the Image3D):

SeedRandom[10] i3d = 1/4 RandomReal[1, {5, 5, 5}] // Image3D 

Style[Show[{i3d, Graphics3D[{FaceForm[Opacity[.6]], Cuboid[{3, 3, 3}]}]}], RenderingOptions -> {"Graphics3DRenderingEngine" -> "BSPTree"}] 

The option RenderingOptions -> {"Graphics3DRenderingEngine" -> "Software"} produces the same but seems to be even slower.

An attempt to Export this as PNG with ImageSize -> {2400, 1600} crashed my video driver and I got not responding FrontEnd taking 100% CPU time of one of my cores. So at least my graphical card doesn't allow to render such a large image.

As a workaround you can try to apply an incremental rendering technique. This post of mine (see the "EDIT 4" section) shows Inset-based approach, another method is suggested by Vitaliy Kaurov (search for "3dImagePartitionExport.nb" in this Wolfram Community thread).

With Mathematica 10.4.1 on Windows 7 x64 I get FrontEnd crash with your code by default but switching to "Graphics3DRenderingEngine" -> "BSPTree" produces the expected output whish is relatively responsible (comparing to the Image3D):

SeedRandom[10] i3d = 1/4 RandomReal[1, {5, 5, 5}] // Image3D 

Style[Show[{i3d, Graphics3D[{FaceForm[Opacity[.6]], Cuboid[{3, 3, 3}]}]}], RenderingOptions -> {"Graphics3DRenderingEngine" -> "BSPTree"}] 

The option RenderingOptions -> {"Graphics3DRenderingEngine" -> "Software"} produces the same but seems to be even slower.

An attempt to Export this as PNG with ImageSize -> {2400, 1600} crashed my video driver and I got not responding FrontEnd taking 100% CPU time of one of my cores. So at least my graphical card doesn't allow to render such a large image.

As a workaround you can try to apply an incremental rendering technique. This post of mine (see the "EDIT 4" section) shows Inset-based approach, another method is suggested by Vitaliy Kaurov (search for "3dImagePartitionExport.nb" in this Wolfram Community thread).

With Mathematica 10.4.1 on Windows 7 x64 I get FrontEnd crash with your code by default but switching to "Graphics3DRenderingEngine" -> "BSPTree" produces the expected output which is relatively responsible (comparing to the Image3D):

SeedRandom[10] i3d = 1/4 RandomReal[1, {5, 5, 5}] // Image3D 

Style[Show[{i3d, Graphics3D[{FaceForm[Opacity[.6]], Cuboid[{3, 3, 3}]}]}], RenderingOptions -> {"Graphics3DRenderingEngine" -> "BSPTree"}] 

The option RenderingOptions -> {"Graphics3DRenderingEngine" -> "Software"} produces the same but seems to be even slower.

An attempt to Export this as PNG with ImageSize -> {2400, 1600} crashed my video driver and I got not responding FrontEnd taking 100% CPU time of one of my cores. So at least my graphical card doesn't allow to render such a large image.

As a workaround you can try to apply an incremental rendering technique. This post of mine (see the "EDIT 4" section) shows Inset-based approach, another method is suggested by Vitaliy Kaurov (search for "3dImagePartitionExport.nb" in this Wolfram Community thread).

With Mathematica 10.4.1 on Windows 7 x64 I get FrontEnd crash with your code by default but switching to "Graphics3DRenderingEngine" -> "BSPTree" produces the expected output whish is relatively responsible (comparing to the Image3D):

SeedRandom[10] i3d = 1/4 RandomReal[1, {5, 5, 5}] // Image3D 

Style[Show[{i3d, Graphics3D[{FaceForm[Opacity[.6]], Cuboid[{3, 3, 3}]}]}], RenderingOptions -> {"Graphics3DRenderingEngine" -> "BSPTree"}] 

The option RenderingOptions -> {"Graphics3DRenderingEngine" -> "Software"} produces the same but seems to be even slower.

An attempt to Export this as PNG with ImageSize -> {2400, 1600} crashed my video driver and I got not responding FrontEnd taking 100% CPU time of one of my cores.

With Mathematica 10.4.1 on Windows 7 x64 I get FrontEnd crash with your code by default but switching to "Graphics3DRenderingEngine" -> "BSPTree" produces the expected output whish is relatively responsible (comparing to the Image3D):

SeedRandom[10] i3d = 1/4 RandomReal[1, {5, 5, 5}] // Image3D 

Style[Show[{i3d, Graphics3D[{FaceForm[Opacity[.6]], Cuboid[{3, 3, 3}]}]}], RenderingOptions -> {"Graphics3DRenderingEngine" -> "BSPTree"}] 

The option RenderingOptions -> {"Graphics3DRenderingEngine" -> "Software"} produces the same but seems to be even slower.

An attempt to Export this as PNG with ImageSize -> {2400, 1600} crashed my video driver and I got not responding FrontEnd taking 100% CPU time of one of my cores. So at least my graphical card doesn't allow to render such a large image.

As a workaround you can try to apply an incremental rendering technique. This post of mine (see the "EDIT 4" section) shows Inset-based approach, another method is suggested by Vitaliy Kaurov (search for "3dImagePartitionExport.nb" in this Wolfram Community thread).