<Button Margin="145,152,144,102" Padding="5,5,5,5" HorizontalAlignment="Center" VerticalAlignment="Center" MouseDown="Button_MouseDown" Height="57" Width="214">
    <WrapPanel>
        <WrapPanel HorizontalAlignment="Center" VerticalAlignment="Center"></WrapPanel>
        <TextBlock Foreground="Black" FontSize="24" MouseDown="TextBlockFirst_MouseDown" >First  </TextBlock>
        <TextBlock Foreground="Red" FontSize="24"   MouseDown="TextBlockSecond_MouseDown">Second </TextBlock>
        <TextBlock Foreground="Blue" FontSize="24"  MouseDown="TextBlockThird_MouseDown" >Third  </TextBlock>
    </WrapPanel>
</Button>

private void TextBlockFirst_MouseDown(object sender, MouseButtonEventArgs e)
{
    MessageBox.Show("You click on first");
}

private void TextBlockSecond_MouseDown(object sender, MouseButtonEventArgs e)
{
    MessageBox.Show("You click on second");
}

private void TextBlockThird_MouseDown(object sender, MouseButtonEventArgs e)
{
    MessageBox.Show("You click on third");
}

private void Button_MouseDown(object sender, MouseButtonEventArgs e)
{
    // This event not working good
    // only middle & right mouse buttons are recognized
    MessageBox.Show("You click on the button");
}

<Button PreviewMouseDown="Button_MouseDown">
   .......
</Button>

private void Button_PreviewMouseDown(object sender, MouseButtonEventArgs e)
{
    if (!(e.OriginalSource is TextBlock))
    {
        MessageBox.Show("You click on the button");
    }
    else
    {
        switch ((e.OriginalSource as TextBlock).Text)
        {
            case "First":
                MessageBox.Show("You click on first");
                break;
            case "Second":
                MessageBox.Show("You click on second");
                break;
            case "Third":
                MessageBox.Show("You click on third");
                break;
        }
    }
}

<Button PreviewMouseDown="Button_PreviewMouseDown" Height="57" Width="214">
    <WrapPanel>
        <WrapPanel HorizontalAlignment="Center" VerticalAlignment="Center"/>
        <TextBlock Foreground="Black" FontSize="24">First</TextBlock>
        <TextBlock Foreground="Red" FontSize="24">Second</TextBlock>
        <TextBlock Foreground="Blue" FontSize="24">Third</TextBlock>
    </WrapPanel>
</Button>