Which type of cost increases continuously with the increase in production?

Variable cost varies at different level of output, this implies that when the output of a particular firm is at zero, the variable cost will be zero and when there is increase in production of output, there will also be a corresponding increase in the variable cost.

Fixed cost is wrong because it remains constant irrespective of the change in the level of production. The marginal cost interact only with the variable cost, it is the cost added by producing one additional unit of a product.
The average cost is total cost of production of a commodity expose by a firm divided by the number of output.