What is the storage cost for a boxed primitive in Java?

It's more than that.

Every object reference has additional overhead, such as a Class reference. Not only that, your 4-byte pointer isn't quite accurate. It's a reference, so it's an ID plus a pointer, AND that pointer may be 8 bytes if you are on a 64 bit JVM.

There also appear to be VM implementation differences. Best way to be sure on this would be to pull it up in a profiler.

My (Super SWAG) estimate would be. Object reference 16 bytes (64 bit JVM) Class reference 16 bytes primitive value 4 bytes (Assuming int.) Total. 36 bytes.

EDIT: Now that your specify 32-bit JVM my SWAG would be 20 bytes using same math above.

This is implementation defined, so there's no specific answer. But I should be able to answer it for Hotspot.

What you need to know is: Hotspot always aligns objects on 8byte boundaries. Furthermore there are 2 words overhead for each and every object. [1]

If we put this together we get:

32bit VM: 4byte integer + 2 words object header = 12bytes. That's no multiple of 8 so as a result the cost for 1 integer is the next multiple of 8: 16byte.

64bit VM: 4byte integer + 2 words = 20bytes. Rounding up again: 24byte size.

The size of a reference obviously does not play into the size of an object itself, except if it has references to other objects which isn't the case for a simple int wrapper. If it would, we'd have 4byte per reference for 32bit and 4byte for heaps <= 32gb with CompressedOops on modern JVMs (otherwise 8byte) for 64bit JVMs.

[1] Interested people can look at the code in share/vm/oops/oop.hpp