I think you might be able to get this work with SP_MSForEachDB still. I've got a script to get a list of all DBs and any orphaned users in them. To make it easier to read, it includes the name of the DB by saving the DB name as a variable.

So possibly with your code this:

EXEC master.sys.sp_MSforeachdb

N'

declare @dbname sysname

set @dbname = ''?''

INSERT INTO Dba_admin.dbo.databaseDataFileSize

SELECT @dbname, SUM(size) * 8, cast(getdate() as date), cast(getdate() as time)

FROM [?].sys.database_files

WHERE type = 0;'

might work.