Very handy and easy operation, performed successfully on a Windows 7 64 bit box without ANY issue.
First, you go in Settings of the VM in VirtualBox and in Storage Section, remove the VDI Virtual HDD from the storage controller of the VM as shown in the picture below.
Then, you open a Terminal session, position in the VM directory and type the command:
VBoxManage modifyhd <name_of_the_VDI_file>.vdi --resize <new_size_you_want_in_megabytes>
You can follow the progression with the command output, which should be similar to the example reported below:
VBoxManage modifyhd ObsoleteOS.vdi --resize 50000 0%...10%...20%...30%...40%...50%...60%...70%...80%...90%...100%
Once the command completes, remember to reattach the VDI to the VM before powering up.
When Windows boots up again, right click on Computer and select Manage to see the new disk space active and shown as an Unallocated partition.
To extend the current partition to match the new space, you need to use external softwares such as the free (for Home use) Easeus Partition Manager.