you should try this:
$array = [
0 => [
"addition_price" => [
0,
40,
40
]
],
1 => [
"addition_price" => [
100
]
],
];
foreach ($array as $key=>$value) {
if(!empty($value['addition_price']) && is_array($value['addition_price'])){
echo $key. " => " .array_sum($value['addition_price']). "<br>";
}
}