import numpy as np

def calculate(list):
    if len(list) != 9:
        raise ValueError("List must contain nine numbers.")
    list = np.array(list).reshape(3, 3)
    result = {
        "mean": [np.mean(list, axis=0).tolist(), np.mean(list, axis=1).tolist(), np.mean(list)],
        "variance": [np.var(list, axis=0).tolist(), np.var(list, axis=1).tolist(), np.var(list)],
        "standard deviation": [np.std(list, axis=0).tolist(), np.std(list, axis=1).tolist(), np.std(list)],
        "max": [np.max(list, axis=0).tolist(), np.max(list, axis=1).tolist(), np.max(list)],
        "min": [np.min(list, axis=0).tolist(), np.min(list, axis=1).tolist(), np.min(list)],
        "sum": [np.sum(list, axis=0).tolist(), np.sum(list, axis=1).tolist(), np.sum(list)]
    }

    return result