Laravel - define multi table relationships

I'm new to laravel and have to define relationships for 3 tables. The tables are events, categories, packages.

Event can have multiple categories and each category can have multiple packages. Same categories can be in various events.

So far i have following tables but not sure if i'm taking the right approach:

Table:events
id - int
title - varchar ...

Table: categories
id - int
name - varchar

Table:packages
id - int
name - varchar
price - decimal

Table:category_package
category_id - int
package_id - int

Table:event_package
event_id - int
package - id int

Inside package model i have:

public function categories()
{
    return $this->belongsToMany('\App\Category');
}

public function events()
{
    return $this->belongsToMany('\App\Event');
}

Inside event and category model i have:

public function packages()
{
    return $this->belongsToMany('\App\Package');
}

I'd like to get the following result out when i query for specific event with its relationships:

[
   "events" => [
        "id" => 1,
        "title" => "whatever title",
        "categories" => [
            [
            "id" => 1,
            "name" => "the category",
            "packages" => [
                ["id" => 1, "name" => "pack1"],
                ["id" => 2, "name" => "pack2"],
                ["id" => 3, "name" => "pack3"]
            ]],
            [
            "id" => 2,
            "name" => "second cat",
            "packages" => [
                ["id" => 4, "name" => "pack4"],
                ["id" => 5, "name" => "pack5"],
                ["id" => 6, "name" => "pack6"]
            ]],
        ]
    ]
]

Is this possible in laravel and how would i go about it. I'm pretty sure I didn't take correct approach.

Thanks

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