Delete All Tables With Dates By Date
You should try printing your commands when they yield errors. If you issued this instead of executing it:

PRINT @cmd;


You would see that this:

WHERE ValueDate BETWEEN ' + CONVERT(VARCHAR,@b,121) + ' AND ' + CONVERT(VARCHAR,@E,121)


Yields this:

WHERE ValueDate BETWEEN 2012-07-01 AND 2014-01-25


Which, since those look to SQL Server like three integers with a couple of subtraction operators, becomes:

WHERE ValueDate BETWEEN 2004 AND 1988


Which isn't even a valid BETWEEN operation, even if it could translate those to dates.

What you should be doing is passing these as proper parameters, e.g.

SET @cmd = 'DELETE FROM dbo.DateTable -- always use SCHEMA prefix
 WHERE ValueDate BETWEEN @b AND @e;';

EXEC sp_executesql @cmd, N'@b DATE, @e DATE', @b, @e;


If any of these columns are DATETIME, not DATE, you really should not be using BETWEEN at all. Instead:

WHERE ValueDate &gt;= @b AND ValueDate &lt; DATEADD(DAY, 1, @e);


Please read:


https://sqlblog.org/2009/10/09/bad-habits-to-kick-declaring-varchar-without-length
https://sqlblog.org/2009/10/11/bad-habits-to-kick-avoiding-the-schema-prefix
https://sqlblog.org/2011/10/19/what-do-between-and-the-devil-have-in-common
https://sqlblog.org/2009/09/03/ladies-and-gentlemen-start-your-semi-colons


As for the overall requirement of repeating this query against all date columns in the database, here is how I would do it (I've looked at the SO question you reference, and it just shows how to do this for one table):

DECLARE @b DATE = '2012-07-01', @e DATE = '2014-01-25', 
        @sql NVARCHAR(MAX) = N'';

SELECT @sql += N'
DELETE ' + QUOTENAME(s.name) 
 + '.' + QUOTENAME(t.name) + '
  WHERE ' + QUOTENAME(c.name) + ' &gt;= @b
  AND ' + QUOTENAME(c.name) + ' &lt; DATEADD(DAY, 1, @e);'
 FROM sys.tables AS t
 INNER JOIN sys.schemas AS s
 ON t.[schema_id] = s.[schema_id]
 INNER JOIN sys.columns AS c
 ON t.[object_id] = c.[object_id]
 WHERE c.system_type_id IN (40,42,43,58,61);
       -- or just = 40 if you're only interested in DATE columns

PRINT @sql;
-- EXEC sp_executesql @sql, N'@b DATE, @e DATE', @b, @e;