I found the answer.
I should bind the Text to parent, then bind to the Class.
<DataGridTemplateColumn Header="Text" IsReadOnly="False" Width="38*">
<DataGridTemplateColumn.CellTemplate>
<DataTemplate>
<TextBox
Text="{Binding Path=TheText, Mode=TwoWay, UpdateSourceTrigger=PropertyChanged}"
Template="{DynamicResource TextBoxOfCellsInDataGridOfSubtitle}"/>
</DataTemplate>
</DataGridTemplateColumn.CellTemplate>
</DataGridTemplateColumn>
<ControlTemplate x:Key="TextBoxOfCellsInDataGridOfSubtitle" TargetType="TextBox">
<TextBox Text="{TemplateBinding Text}"
AcceptsReturn="False"
CaretBrush="White"
Foreground="White"
Background="Transparent"
BorderBrush="Transparent"
BorderThickness="0"
TextAlignment="Center"
HorizontalAlignment="Stretch"
HorizontalContentAlignment="Stretch"
VerticalAlignment="Stretch"
VerticalContentAlignment="Center"/>
</ControlTemplate>