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As you have using Factory and there is not the meaning of use o CustomAttribute

You can save using dice_sum and place_of_birth using seter function like

$customer->setDiceSum('9999');
$customer->setPlaceOfBirth('dome');

So, you have to replace

$customer = $this->_customerFactory->create();
$customer->setWebsiteId(1);
$customer->setFirstname($data['firstname']);
$customer->setLastname($data['lastname']);
$customer->setPassword($data['password']);
$customer->setGender($data['gender']);
$customer->setDob($data['dob']);
$customer->setEmail($data['email']);
$customer->save();
$customer = $this->_customerRepoInterface->getById($customer->getId());
$customer->setCustomAttribute('dice_sum', '23');
$customer->setCustomAttribute('place_of_birth','joan');
$this->_customerRepoInterface->save($customer);

BY

$customer = $this->_customerFactory->create();
$customer->setWebsiteId(1);
$customer->setFirstname($data['firstname']);
$customer->setLastname($data['lastname']);
$customer->setPassword($data['password']);
$customer->setGender($data['gender']);
$customer->setDob($data['dob']);
$customer->setEmail($data['email']);
$customer->setDiceSum('9999');
$customer->setPlaceOfBirth('dome')
$customer->save();

BEST SOLUTION:

If you have used service provider class means RepositoryInterface, Then I suggest to you use service provider for create the new customer.

<?php

namespace Exchanges\Test\Test;

/**
 * Description of customerCustomAttribute
 *
 */
class customerCustomAttribute {

    /**
     * @var \Magento\Customer\Api\CustomerRepositoryInterface
     */
    protected $customer;

    /**
     * @var \Magento\Customer\Api\Data\CustomerInterface
     */
    protected $customerData;

    public function __construct(
    \Magento\Customer\Api\CustomerRepositoryInterface $customer,
    \Magento\Customer\Api\Data\CustomerInterface $customerData      
    ) {
        
        $this->customerData = $customerData;
        $this->customer = $customer;
    }
    public function saveCustomer()
    {
        $customer =  $this->customerData;
        $customer->setWebsiteId(1);
        $customer->setFirstname($data['firstname']);
        $customer->setLastname($data['lastname']);
        $customer->setPassword($data['password']);
        $customer->setGender($data['gender']);
        $customer->setDob($data['dob']);
        $customer->setEmail($data['email']); 
        $customer->setCustomAttribute('dice_sum', '23');
        $customer->setCustomAttribute('place_of_birth','joan');
        $this->customer->save($customer);
        
    }        
}