I want nested Multi select dropdown in Mudblazor

You can use ToStringFunc property of MudSelect docs. This property can be used to define what part of the object should be displayed as the Text for the selected item.

<MudSelect Margin="Margin.Dense" T="IndicatorDefinition" MultiSelection="true"
            SelectAll="true" SelectAllText="On Prem"
        @bind-SelectedValues="_selectedIndicators"
        ToStringFunc="SelectionToString"
        Style="width: 100px;" Clearable="true">
    @foreach (var indicatorDefinition in IndicatorDefinitions)
    {
        <MudSelectItem Value="@indicatorDefinition" Style="margin-left: 40px !important ;">@indicatorDefinition.SubTitle</MudSelectItem>
    }
</MudSelect>


@code {
    public List<IndicatorDefinition> IndicatorDefinitions { get; set; } = new()
        {
        new () {SubTitle= "Cloud"}, 
        new () {SubTitle= "Hybrid"}
        };
    public IEnumerable<IndicatorDefinition> _selectedIndicators = new List<IndicatorDefinition>();

    public class IndicatorDefinition
    {
        public string SubTitle { get; set; }
        public double Value { get; set; }
    }

    string SelectionToString(IndicatorDefinition value){
        return value.SubTitle;
    }
}

ToStringFunc Snippet

And you can use MultiSelectionTextFunc + ToStringFunc, if you want to have different text based on the selected items list.

<MudSelect Margin="Margin.Dense" T="IndicatorDefinition" MultiSelection="true"
            SelectAll="true" SelectAllText="On Prem"
        @bind-SelectedValues="_selectedIndicators2"
        MultiSelectionTextFunc="GetMultiSelectionText"
        ToStringFunc="SelectionToString"
        Style="width: 100px;" Clearable="true">
    @foreach (var indicatorDefinition in IndicatorDefinitions)
    {
        <MudSelectItem Value="@indicatorDefinition" Style="margin-left: 40px !important ;">@indicatorDefinition.SubTitle</MudSelectItem>
    }
</MudSelect>

@code {
    public List<IndicatorDefinition> IndicatorDefinitions { get; set; } = new()
        {
        new () {SubTitle= "Cloud"}, 
        new () {SubTitle= "Hybrid"}
        };

    public IEnumerable<IndicatorDefinition> _selectedIndicators2 = new List<IndicatorDefinition>();

    public class IndicatorDefinition
    {
        public string SubTitle { get; set; }
        public double Value { get; set; }
    }

    string SelectionToString(IndicatorDefinition value){
        return value.SubTitle;
    }
    string GetMultiSelectionText(List<string> selectedValues){
        if(selectedValues.Count == IndicatorDefinitions.Count){
            return "All On Prem selected";
        }else{
            return string.Join(",",selectedValues);
        }
    }
}

MultiSelectionTextFunc Snippet