Find bounding box of arbitrary 3d graphics?

RegionBounds@RegionUnion[ 
  BoundaryDiscretizeRegion[Cone[]], 
  BoundaryDiscretizeRegion[Cuboid[]]
  ]

{{-1., 1.}, {-1., 1.}, {-1., 1.}}

Charting`get3DPlotRange[
 Show[Graphics3D[{Cone[], Cuboid[]}], PlotRangePadding -> None]]
(*  {{-1., 1.}, {-1., 1.}, {-1., 1.}}  *)

See How to get the real PlotRange using AbsoluteOptions?

If "arbitrary 3d graphics" includes of objects of heterogeneous dimensions, then get3DPlotRange still works:

Charting`get3DPlotRange[
 Show[Graphics3D[{Cone[], Cuboid[], Point[{0, 0, -3}], 
    Line[{{1, 0, 0}, {-2, 0, 0}}]}], PlotRangePadding -> None]]
(*  {{-2., 1.}, {-1., 1.}, {-3., 1.}}  *)

MinMax /@ Transpose[RegionBounds /@ {Cone[], Cuboid[]}]

{{-1, 1}, {-1, 1}, {-1, 1}}